I can’t get my son to sleep in his bassinet

My son is 5 weeks old and we are struggling with sleeping at night. He sleeps in three hour stretches. Every night for his first stretch of sleep he will usually (90% of time) stay in his bassinet. After his next bottle he will sleep in his bassinet for maybe an hour and he wakes up and refuses to go back to sleep in his bassinet. I’ve tried giving him his binky and patting his back. I’ve tried rocking him and putting him back in his bassinet after he falls asleep but he will wake up within a few minutes. The only way I can get him to sleep is on my chest. I know that it’s not safe sleep. But I’m exhausted and I need sleep too. I don’t know how to get him to stay in his bassinet. I would love any advice.