Is it true that if you sanitize your hands and then touch an object after, that object is now sanitized too?

I feel like this isn’t true. I feel like you would just get whatever germ is on that item after you’ve touched it. I’m currently pregnant and I was out with my mother in law and we ordered a coffee. I went to sanitize the cup and she said “just sanitize your hands. Once you do that the cup will already be sanitized once you touch it” I said “really? Are you sure I thought you have to sanitize everything” she said “yes, I wouldn’t put my grand baby at risk if I wasn’t sure”

Is this true???