S.B.
Your baby is used to sleeping with you and I hate to tell you this, but there is going to be crying involved when you try to change that.
Have you tried getting her used to her crib during the day? I don't mean leaving her in there, but when you go to the bathroom, lay her down. When you get out of the shower and get dressed, lay her down. She may cry, but you can call out to her that you hear her and you'll be right there. She won't understand your words, but it's the tone of your voice. Her crib is a happy place. It's okay.
You might need to try putting her down before she's in a deep sleep and rubbing her back and humming to her. She may fuss a bit, but it's not torturing her.
When I had my first baby, there wasn't really a term "cry it out". There was no stigma or guilt associated with knowing that babies cry. My kids would literally sleep anywhere because I got them used to being in different places, especially in their cribs. That's not to say we never cuddled or they didn't sleep with me sometimes, but they were comfortable sleeping by themselves. It takes a little time. My daughter loved cuddling, but when it came to sleeping, she was much happier sleeping by herself. My son could fall asleep getting his diaper changed.
Just ease your baby into getting used to laying down other places so that they feel familiar to her and again, don't wait for her to be sound asleep to lay her down. That will startle her and she will cry.
A little crying isn't a bad thing though. It really isn't.
I wish you the best!