Frame

main.py

# built-in imports should be at the top
# but sys is not even needed! See last block.
# import sys

# Module imports are preferred! Unneeded items should not be imported
from PySide2 import QtCore, QtWidgets

# numbers that are used multiple times or are key to the functionality
# should be in 1 place so one doesn't need to dig for the settings.
SIZE_SMALL = 70
SIZE_BIG = 200
# human reaction time is around 200ms, I'd stick to that for such transitions.
DURATION = 200


class MyWidget(QtWidgets.QWidget):
    def __init__(self):
        super().__init__()
        self.setWindowTitle('Conversor de arquivos')
        # x, y, w, h -> esquerda, topo, largura, altura
        self.setGeometry(300, 100, 900, 600)

        # if you set both width & height, use setMinimumSize
        self.setMinimumSize(700, 500)

        # you can pass self so you don't need setLayout
        self.vbox_main = QtWidgets.QVBoxLayout(self)

        self.hbox_main = QtWidgets.QHBoxLayout()
        self.hbox_main.setContentsMargins(0, 0, 0, 0)
        self.hbox_main.stretch(1)

        self.button_toggle = QtWidgets.QPushButton('TOGGLE')
        self.button_toggle.setMaximumSize(100, 40)
        self.button_toggle.clicked.connect(self.toggle)

        self.frame_left_menu = QtWidgets.QFrame()
        self.frame_left_menu.setStyleSheet('background-color: green')
        # Max size 16777215 is default, you just need the width to be set
        # self.frame_left_menu.setMaximumSize(QtCore.QSize(70, 16777215))
        self.frame_left_menu.setMaximumWidth(SIZE_SMALL)

        self.vbox_menu_left = QtWidgets.QVBoxLayout(self.frame_left_menu)
        self.vbox_menu_left.setSpacing(5)

        self.frame = QtWidgets.QFrame()
        self.frame.setStyleSheet('background-color: yellow')
        # Why?
        # self.frame.setMinimumWidth(16777215)

        # Add objects to layouts

        # I'd use a loop for these
        for i in range(1, 5):
            button = QtWidgets.QPushButton(f'BTN{i}')
            self.vbox_menu_left.addWidget(button)

        self.hbox_main.addWidget(self.frame_left_menu)
        self.hbox_main.addWidget(self.frame)

        self.vbox_main.addWidget(self.button_toggle)
        self.vbox_main.addLayout(self.hbox_main)

        # create the anim object once, just trigger it when needed in toggle()
        self.animation = QtCore.QPropertyAnimation(self.frame_left_menu, b'minimumWidth')
        self.animation.setDuration(DURATION)
        self.animation.setEasingCurve(QtCore.QEasingCurve.InOutCubic)

    def toggle(self):
        current_width = self.frame_left_menu.width()
        if current_width == SIZE_SMALL:
            # use 1 naming style
            width_extended = SIZE_BIG
        else:
            width_extended = SIZE_SMALL

        self.animation.setStartValue(current_width)
        self.animation.setEndValue(width_extended)
        self.animation.start()


if __name__ == '__main__':
    app = QtWidgets.QApplication([])
    widget = MyWidget()
    # Have only 1 spot where the size is set!
    # This would even set it smaller than the set minimum size!
    # widget.resize(400, 300)
    widget.show()
    # just use QApplication.exec_ here. No need for sys.exit. happens anyway.
    app.exec_()

Thank you!