Help a mama out freshly postpartum

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Hi ya'll ,im in desperate need of help. My newborn wont sleep on his basinet/crib. I believe its becauseof the surface of the "mattress padding" its hard like.sleeping on the hardwood floor, he would rather sleep well on his swing and i cant have him sleep there and hes not completely on his back flat. Idk how to make the basinet softer in.a safe way for him to stay like being there. For reference i have the halo bassinest swivel sleeper.