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The answer is : it is impossible to compute a BEV of a scene if you do not have distance-related information about the pixels of your image.

Think about it : imagine you have the picture of a vertical screen : the Bird's Eye View would then be a line. Now say that this screen is displaying the image of a landscape and that the picture of this screen is indistinguishable from a picture of the landscape itself. The BEV would still be a line (a colorful one though).

Now, imagine you have the exactly the same picture, but this time it's not a picture of a screen but of the landscape. Then, the Bird's Eye View is not a line and is closer to what we usually imagine a BEV to be.

Finally, let me state that OpenCV has no way to know if your picture is describing a plane of something else (even given camera parameters), therefore, it cannot compute the BEV of your scene. The function cv2.perspectiveTransform needs you to pass it a homography matrix (you may obtain one using cv2.findHomography(), but you will need some distance information about your image as well).

Sorry about the negative answer, but there's no way to solve your problem given only the intrinsic and extrinsic calibration matrices of the camera.