4 week old sleeping on tummy?

So I'm pretty sure my 4 week old has colic seeing as she cries for seemingly no reason for hours on end, usually at night when my husband and I are trying to go to bed. I googled ways to soothe a colicky baby and one suggestion was to lay the baby on their tummy across your lap, and then pat/rub their back. As soon as I did that, she immediately calmed down. I tried twice to flip her back over so I could move her to the cradle and go to bed, but as soon as I flipped her she started crying again. I then just moved her, still tummy down, to the couch next to me, and she's sleeping peacefully.

I know safe sleep rules are to never put baby to sleep on their tummy, but if she starts screaming the second I flip her, and she's only calm on her tummy, can I let her sleep on her tummy?

(Also no the blanket she's laying on is not blocking her face or airways, but I'd be moving her to her cradle where there is no blanket anyway)

Edit:

I didn't let her sleep on her tummy. I moved her to her cradle and let her lay on her tummy for a few seconds to get used to the new surface and flipped her over to her back and she slept just fine after that. Thank you for all your comments