Noise or no noise?

My LO is 4.5 months old and sleeps only when there is complete silence. She has been like this since birth. She would wake up when anyone opened or closed our hospital room door. The LO gets overstimulated with anything and everything so if she hears anything in her sleep she wakes right up as if she never slept. She really had a hard time sleeping so i started to make sure she gets silence when she is sleeping. Tried white noise but didn’t work. This means i need to stop everything when she is napping.

Now it makes me wonder whether i did the right thing. Ideally i would like her to get used to the noise but after numerous failed attempts, i gave up.

What do you all do? How do i break this?