Baby Won’t Sleep in Bassinet 😩

Hi ladies. My baby is 4 weeks old tomorrow. He has never successfully slept for a long period of time in his bassinet. We’ve tried over and over, using white noise, swaddling, putting him down when he’s drowsy, etc. NOTHING works. He screams after being put down for 3 minutes. However, if I’m awake, I let him nap in the bed beside me while I watch tv and he sleeps perfectly fine. I don’t know what to do anymore. I don’t want to cosleep because the bed is not big enough for me and my fiancé and the baby, and I don’t want to risk suffocation or him falling off the bed. I’m at a loss. This is how he sleeps when he’s next to me in the bed. Out like a light 🙄 Don’t worry, I never fall asleep or leave him in the bed with a pillow that close to his face. I’m literally awake watching tv lol.