Getting baby to sleep in crib

She is 3 months old.

She’s been sleeping in bed with me and my SO since 1 1/2 months. I already tried to put her in her bassinet when she was asleep.

But she always woke up after 20 minutes. I thought it’d be different with her crib but it’s the same thing. She’ll be asleep and wake up SCREAMING. But she’ll fall asleep in my bed fine. Is her bed too cold or hard? How do I get her to sleep in it?

I try to put her in there awake. And I stand by the crib so she doesn’t feel alone. But idk what else to do.