That's not fully correct.
You push the pedal till all brake pads lay on the disc.
After this you will get pressure in the system.
All what happens now, is that brake lines/pipes, brake calipers (!) etc. will deform.
This you feel in the pedal (it's soft etc.).
Master brake piston size -> the lift you have to make till the pressure can raise.
Main problem: When you change the piston size of the brake too much you will raise the force on the brake pad and this force is important for your deceleration.
This raised force will also deform the caliper more - soft pedal.
vice versa: good caliper -> hard pedal :-)
And now I have one question Kerz, what Piston size the Uno 4pot calipers had which I bought, years ago?
I hope this winter I can install them...
I will also update the rear brake system (better looking), and I have to do some calcs - but calipers are ~550km far away from me