With DS, when he was in the bassinet, I'd nurse him & then I'd swaddle him. Then I'd walk him around the dimly lit room till he fell asleep, then put him down. Gradually, I'd walk him less & less, and put him down sooner & sooner, so that he was just drowsy when I put him down.
Then once he was in his crib, we weren't swaddling anymore, so I'd just nurse him, he'd get drowsy from that & I'd be able to just walk him from the glider & right into his crib.
For naps, we used the swing, so that would rock him to sleep.
DD is different since she isn't swaddled & sleeps on her belly. For her, I started with naps, by just putting her in her swing at the first yawn & letting her fuss to sleep. She falls asleep in under 5 minutes. (If there's a case where her fuss escalates to crying, I go back in, take her out & kinda start over.)
So now for nighttime, I can put her down in the bassinet drowsy & she falls asleep w/o fussing b/c I think she got used to falling asleep on her own for naps. She just started this about a week or so ago.
I'm not sure any of that helps since it seems like you're doing bottles & LO is at daycare. But, I guess the main point is to do a routine where you can gradually work toward LO being drowsy, but awake when you put him down. Maybe you can ask your DCP to rock him less & less & see if he starts to go to sleep on his own, or whatever, so that it's consistent with what you're doing at home.