Can I damage my iPhone 13 Pro Max by pressing to hard on the screen?

Almost certainly not. The iPhone 13 can take around several hundred Newtons of force before cracking, which is far beyond what a push with two fingers could do.

It only takes a light touch to navigate the iPhone screen. What kind of damage are you speaking of.

The only way for you to damage the screen with a finger would be if you were trying to do it deliberately. The display is very strong.

It's possible, but I can't imagine it from normal use.