Baby sleeping on tummy

My 5 week old is so fussy tonight & eveytime I try to put her on her back she immediately gets upset and starts crying, I have tried rocking her, just everything she falls asleep & as soon as I put her down she wakes up instantly or a few minutes later but when I tried putting her on her tummy she knocked right out & i am terrified of putting her on her tummy like this because of SIDS but she’s sleeping so well & I am exhausted so what do I do & has any other parent let their newborn sleep on their tummy