Tummy sleeping

Hey ladies! My LO is 5 weeks and likes to sleep on his stomach. When he sleeps on my chest he's on his belly and he will pass out during tummy time. Right now he really only sleeps on my chest at night and a little in his swing. I want to put him in his bassinet tonight on his stomach. Does anyone have a tummy sleeper that has done the same thing this early. Note:he can turn his head from side to side. TIA.