Does she seem uncomfortable sleeping on her back? My baby was a contact napper until 6 months as needed to sleep upright due to wind and reflux secondary to cow's milk protein intolerance so once we finally sorted her milk and this resolved she was actually able to physically sleep lying down without being propped upright in my arms but still needed to be taught how. So if no physical reasons then just needs some teaching.
Started form of gradual retreat every couple of days so started holding her half in arms, half on bed and shhhhhing to sleep after rocking a bit to drowsy. Then rocking and shhhhhing laid next to in bed with some contact with my body then completely away from me but let her play with a comforter or your hands until knocked out whilst shhhhhing and stroking head/chest if wish. Once at the point of able to sleep in bed alongside you without rocking or contact (except playing with hands/comforter or replacing dummy if have) then move to nursery with blackout blinds and curtains. Into cot awake but drowsy, allow to play with hands/comforter until asleep with me sitting in chair. Wasn't sitting yet so cot still on upper level so not too much strain on back as could take 30 mins. Replace dummy if falls out and using. Once doing this consistently then reduce intervention so just cuddle then laid down with comforter and allow to roll around until asleep whilst sitting in chair shhhhhing. Once doing this consistently then withdraw from room before asleep and see. Accept may whinge a little. Watch on monitor, if crying/properly upset then back in chair and retry after a few days/week.
Do this for all naps and sleep as will work much faster. My husband didn't like sitting for the 30mins for bedtime so kept holding her and putting down asleep. Wasn't until he started following method that her self soothing sped up drastically.
Now we are at the point that routine is wait until ready for bed, nappy change etc then curtains/blinds drawn, sing a song (twinkle twinkle little star for us) whilst cuddling in sleeping bag and swaying for a minute or so until doing slow blinks then down in cot, 5-10 head strokes/back strokes whilst shhhhhing depending on position then out of door. Then will fall asleep after some rolling around, sometimes bit of whingeing as drops off.
For us no crying, though we used a dummy which helped for sure. Game changer definitely when started being able to replace own dummy! Also using a comforter to promote self-soothing without you. Now sleeps through consistently since about 8.5 months after period of one wake up until dropped to 2 naps. Bit drawn out but worth it for independent sleep with no controlled crying/cry it out. I buggered my shoulder propping her up for the contact naps so was very happy to see them go ngl! You may be able to skip some steps as we did it very slowly tbh.