Как мне скрыть из layout widget до тех пор пока не запустится анимация?

Тяжелый код. Чтобы немного понять, что происходит, я отключил app.setStyleSheet(StyleSheet) и установил в некоторых местах setStyleSheet, чтобы видеть где-какой виджет.

Убрал menu_layout.addWidget(self.menu_pos[i]), т.к. управлять геометрией в макете не возможно.

Обратите внимание на расчет pos1 и pos2 и др. отмеченное в тексте.

Пробуйте.

import sys
import os                                                            
from PyQt5 import QtWidgets, QtGui, QtCore
from PyQt5.QtCore import (QCoreApplication, QMetaObject, QObject, QPoint,
    QRect, QSize, QUrl, Qt, QPropertyAnimation)
from PyQt5.QtWidgets import QGraphicsEffect, QApplication, QWidget, QMainWindow,\
     QVBoxLayout, QLabel
from PyQt5.QtQml import QQmlApplicationEngine

DIR_PATH = os.path.dirname(os.path.realpath(__file__))               


#class test_mynu(QtWidgets.QWidget):
class Test_Menu(QtWidgets.QWidget):
    def __init__(self, arr="", parent=None):
        super(Test_Menu, self).__init__(parent)
        self._expand = False      
        self.setStyleSheet('background:#0f0; color:#000;')                        # + уберете      
        self.menu_pos_block = QtWidgets.QWidget(maximumWidth=30, minimumWidth=0)
        blur = QtWidgets.QGraphicsBlurEffect(blurRadius=1)                        # 5 установите свое
        self.menu_pos_block.setGraphicsEffect(blur)
        #------menu_pos_block_layout------
        self.menu_pos_block_layout = QtWidgets.QHBoxLayout(self.menu_pos_block)
        self.menu_pos_block_layout.setObjectName(u"menu_pos_block_layout")
        #------menu_pos_label------
        self.menu_pos_label = QtWidgets.QLabel()
#        self.menu_pos_label.setText(arr)
        self.menu_pos_label.setText(arr[-2:])                                     # установите свое
        self.menu_pos_block_layout.addWidget(self.menu_pos_label)
        #------ADD------
        lay = QtWidgets.QHBoxLayout(self)
        lay.addWidget(self.menu_pos_block)


class MainWindow(QtWidgets.QMainWindow):

    def num(self):
        return 3

    def __init__(self, widget, parent=None):
        super().__init__(parent)

        self.toggle_animations = QtCore.QSequentialAnimationGroup(self)
        self.toggle_animation  = QtCore.QParallelAnimationGroup(self)

        centralwidget = QtWidgets.QWidget(objectName="centralwidget")
        self.setCentralWidget(centralwidget)
        central_w_layout = QtWidgets.QGridLayout(centralwidget, objectName="central_w_layout")
        vs_up = QtWidgets.QSpacerItem(17, 105, QtWidgets.QSizePolicy.Minimum, QtWidgets.QSizePolicy.Expanding)
        central_w_layout.addItem(vs_up, 0, 1, 1, 1)
        hs_left = QtWidgets.QSpacerItem(327, 20, QtWidgets.QSizePolicy.Expanding, QtWidgets.QSizePolicy.Minimum)
        central_w_layout.addItem(hs_left, 1, 0, 1, 1)
        hs_right = QtWidgets.QSpacerItem(326, 20, QtWidgets.QSizePolicy.Expanding, QtWidgets.QSizePolicy.Minimum)
        central_w_layout.addItem(hs_right, 1, 2, 1, 1)
        vs_down = QtWidgets.QSpacerItem(20, 105, QtWidgets.QSizePolicy.Minimum, QtWidgets.QSizePolicy.Expanding)
        central_w_layout.addItem(vs_down, 2, 1, 1, 1)

        self.block = QtWidgets.QWidget()
        self.block.setObjectName(u"block")

        self.x, self.y = 166, 205                                             # +
        QtCore.QTimer.singleShot(100, self.start_x_y)                         # +++

        self.block.setStyleSheet('background:#f99; color:#00f;')              # + уберете 
        central_w_layout.addWidget(self.block, 1, 1, 1, 1)             

        layout_block = QtWidgets.QVBoxLayout(self.block)
        layout_block.setObjectName(u"layout_block")
        menu_block = QtWidgets.QWidget()
        menu_block.setObjectName(u"menu_block")
        menu_block.setStyleSheet('background:#ff9; color:#0ff;')              # + уберете 
        layout_block.addWidget(menu_block)                         
        #------menu_layout------
        menu_layout = QtWidgets.QHBoxLayout(menu_block)
        menu_layout.setObjectName(u"menu_layout")
        menu_layout.setSpacing(10)                                            # 0 установите свое

        self.menu_but = []
        self.menu_pos = []
        self.menu_by_pos = None

        for i in range(self.num()):
            menu_pos_block = Test_Menu("menu_{}".format(i), self)              # + , self !!!
            menu_pos_block.setObjectName("menu_pos_{}".format(i))
            self.menu_pos.append(menu_pos_block)

# -           self.menu_pos[i].setGeometry(QRect(menu_pos_block.width(), menu_pos_block.height(), 151, 181))            
            self.menu_pos[i].setGeometry(QRect(-10, -10, 0, 0))                # + 
            self.menu_pos[i].show()                                            # +

#            menu_layout.addWidget(self.menu_pos[i])                           # ---

        #------menu_block_but------
        self.menu_block_but = QtWidgets.QWidget()
        self.menu_block_but.setObjectName(u"menu_block_but")
        menu_layout.addWidget(self.menu_block_but)         
        #------menu_block_but_layout------
        menu_block_but_layout = QtWidgets.QVBoxLayout(self.menu_block_but)
        menu_block_but_layout.setObjectName(u"menu_block_but_layout")
        #------menu_but_radio------
        for i in range(self.num()):
            menu_but_radio = QtWidgets.QRadioButton('{}'.format(i))
            menu_but_radio.setObjectName("{}".format(i))
            menu_but_radio.toggled.connect(self.menu_animation)
            self.menu_but.append(menu_but_radio)
            menu_block_but_layout.addWidget(menu_but_radio)

        # conect menu and but
        self.menu_by_but = dict()
        self.but_by_menu = dict()
        for i in range(self.num()):
            but = self.menu_but[i]
            menu = self.menu_pos[i]
            self.menu_by_but[menu] = but
            self.but_by_menu[but] = menu

        menu_block_content = QtWidgets.QWidget()
        menu_block_content.setObjectName(u"menu_block_content")
        menu_layout.addWidget(menu_block_content)     
        #------menu_content_layout------
        menu_content_layout = QtWidgets.QHBoxLayout(menu_block_content)
        menu_content_layout.setObjectName(u"menu_content_layout")
        #------menu_label------
        menu_label = QtWidgets.QLabel()
        menu_label.setText('text, text text, text')
        menu_content_layout.addWidget(menu_label)

        self.num = 0
        self.menu_pos_ter = []
        self.menu_nums = []                                                  # +++

    def menu_animation(self):
        self.num = self.num + 1
        self.toggle_animations.clear()
        num = int(self.sender().objectName())
        self.menu_pos_ter.append(self.menu_pos[num])

        #retutn element с _expand = True
        for menu in sorted(self.menu_pos_ter, key=lambda x: x._expand):
            menu_width  = 74    # menu.width()
            menu_height = 81    # menu.height()
            menu.setMaximumSize(QSize(16777215, 16777215))

            if self.menu_nums:                                                   # +
                self.menu_nums = [self.menu_nums[-1],]                           # +
            self.menu_nums.append(menu)                                          # +

            pos1 = QRect(self.x,               #self.menu_block_but.x() - menu_width, 
                         self.y,               #menu.y(),
                         menu_width,
                         menu_height)

            pos2 = QRect(self.x+200,           #self.menu_block_but.x() + self.menu_block_but.width(), 
                         self.y,               # menu.y(),
                         menu_width,
                         menu_height)
# ???            pos3 = QRect(menu.width(), menu.height(), menu.x(), menu.y())

            anims = QPropertyAnimation(menu, b"maximumWidth")
            anims.setDuration(1000)
            anims.setStartValue(30)
            anims.setEndValue(100)

            but = self.menu_by_but[menu]
            menu.raise_()
            self.menu_block_but.raise_()
            if but.isChecked():
                start_pos = pos1
                end_pos = pos2
            else:
                start_pos = pos2
                end_pos = pos1

            anim = QPropertyAnimation(menu, b"geometry")
            anim.setDuration(1000)
            anim.setStartValue(start_pos)
            anim.setEndValue(end_pos)
            self.toggle_animations.addAnimation(anim)
#?            self.toggle_animation.addAnimation(anims)                      # - ???
            self.toggle_animation.addAnimation(self.toggle_animations)

        if (self.num == 1) or (self.num == 3): 
            self.toggle_animation.start()
            self.menu_pos_ter.clear()
        if self.num == 3 :
            self.num = 1        

# ++ vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv      
    def start_x_y(self):
        self.x, self.y = self.block.x()-100, self.block.y()+20

    def resizeEvent(self, event):
        self.x, self.y = self.block.x()-100, self.block.y()+20
        [ i.move(-100, 0) for i in self.menu_pos]
        for i, menu in enumerate(reversed(self.menu_nums)):
            if i == 0: menu.move(self.x+200, self.y)
            else: menu.move(self.x, self.y)
# ++ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

StyleSheet = """
#centralwidget QWidget QWidget,
#centralwidget QWidget QWidget QWidget QWidget,
#centralwidget QWidget QWidget QWidget QWidget QWidget QWidget,
#centralwidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget,
#centralwidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget{
background:#000;
color:#fff;
}
#centralwidget QWidget,
#centralwidget QWidget QWidget QWidget,
#centralwidget QWidget QWidget QWidget QWidget QWidget,
#centralwidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget,
#centralwidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget QWidget{
background:#fff;
color:#000;
}
#click_me{
background:#000;
color:#fff;
}
"""

if __name__ == "__main__":
    app = QtWidgets.QApplication(sys.argv)
#    app.setStyleSheet(StyleSheet)                                 # !!! установите

    #load qml
    file = os.path.join(DIR_PATH, "qml_window.qml") 
    url = QUrl.fromLocalFile(file)                  
    engine = QQmlApplicationEngine()
    context = engine.rootContext()
    context.setContextProperty("main", engine)
    engine.load(url)

    if not engine.rootObjects():
        sys.exit(-1)

    widget = QWidget.createWindowContainer(engine.rootObjects()[0])
    w = MainWindow(widget)
    w.resize(640, 570) #Size window
    w.show()

    sys.exit(app.exec_())