Argh! That bloody phrase haunted me. we didn't used to co-sleep, but we did used to rock our little boy to fast asleep in our arms and then put him down asleep.
At about 4.5 months, that stopped working - no matter how asleep he seemed, his eyes would ping open as soon as he went into the cot! (B@stard.....!)
Then I found if I put him in the crib "drowsy" and rolled him on to his side, I could pat his bum and shush. When he fell asleep, I'd roll him back on his back. Then that stopped working, and as soon as I'd roll him back he'd wake up.
By then he was 5 months and he could roll both ways, he started sleeping on his side /stomach occasionally anyway, having rolled over in the night. At that point I started to put him in the crib, roll him on his side, pat and shush him to sleep and leave him there.
Now at just about 6 months, I put him down drowsy (which for him is the second he has his eyes closed, and is still, after a cuddle) on his side / front and he grizzles for about 5mins and falls asleep. (Not SIDS recommended, but he does it himself anyway...)
So, it has taken us nearly 2 months to go from fast asleep, gently down and ninja roll out of the room. To dumping him, wandering out and hoping.
There is probably another stage for you, which is going from asleep on you, to asleep in your arms for example, which is where we started. There's so much info online to help. I like weebeedreaming and the baby sleep site. I practiced every nap time, every sleep time, every night waking, every day, and we did get there.
Good luck 🤞🏻