12 day old son is restless and fussy

He sleeps in his bassinet which he hates. The only other things we have are a swing and rock n play and i dont want him sleeping in either for ridk of SIDS but as soon as i put him in his bassinet he gets super fussy and cries. Its every 5 minutes and i cannot get any sleep. I put a thin blanket in his bassinet on the bottom for him to sleep on and im wondering if its a bad idea? Also, any tips u have to help me get him to actually sleep for even 20 minutes helps. We just changed his formula bcuz his old one made him gassy so itll take 3 or so days to notice any difference and if thats affecting his sleep. Hes currently swaddled in his bassinet (bcuz im awake and can watch him) and hes been doing ok but i cant sleep when he does bcuz he cant sleep with blankets. Heres his bassinet with the blanket on bottom.

We also do have a crib but it wont fit in our room and i want him sleeping in my room, as well as we dont have any monitors yet.