Wait until the cord falls off, it could get snagged & end up bleeding.

I believe I was told to wait until the cord fell off but I used to lay my kids on my chest for a couple minutes to do some light tummy time. I think I told myself it was for tummy time. I just like baby cuddles.

For your 1 wk old baby ? Usually recommended by Drs to wait until they can hold their head up to do tummy time at 3-4 month’s of age

My son wouldn't lay any other way, I'd say as long as she has clothes on and it's not touching anything she should be okay. Congrats!!