It's easy to forget what it's like for a baby, who has no experience or prior knowledge to draw on like we do.
As adults we have learnt the art of going to sleep. We know we need to be in a comfortable position. We know that we can only go to sleep if our body is relaxed, so we do things to help ourselves to relax - lie still, calm our breathing, clear our mind and so on.
What you need to bear in mind is that all of this is learnt behaviour. We have learnt through personal experience how to relax our bodies to give ourself the best chance of going to sleep.
A child has not yet learnt this and has no experience, so it's within the role of being a parent to teach it. Some things your child is likely to not know, even though these are obvious to you or I:
● to go to sleep she needs her body to be still
● to go to sleep she needs to physically do nothing with her body (So not "play").
● to go to sleep she needs to be quiet
So, you could do with thinking of gentle, compassionate ways to teach her these skills so that she can go to sleep in the cot.
I'd suggest starting by holding her hands. Both her hands in one of yours gives you another free hand for stroking/patting or whatever. Otherwise one of her hands in each of yours. This physically holds her still, but in a gentle way. It also keeps her lying down.
If she screams, the obvious answer would be encourage dummy sucking for no crying self-soothing. If you don't have this option then you need to sooth her another way and it probably will involve crying, but - importantly - crying while you try to comfort and sooth not being left to cry.
So how to sooth? The best option would be in-cot soothing. You being as physically close to her as you can, calming eye contact, stroking if that helps her, or patting might be good. You're unlikely to get her to stop crying straight away but if you can keep her lying down and still then that's an achievement and she should calm down in the end if you keep at it.
If the above isn't happening or accelerates, then pick her up to calm her down. Hold and comfort her until she calms down. Then put her back down and start again. Don't expect her to not cry (dummy is the only realistic way yo have that happen straight off), but try to calm and sooth her in the cot again. If no luck, pick up again, sooth and put down. Just keep repeating the pick up put down and eventually she will calm.
Over time, this will all get easier, quicker and involve less crying. But initially while you are teaching there might be some crying. But you'll always be there - caring, being compassionate and helping her to learn at her own pace.