Baby won’t do tummy time

First off I’m a new mom with my first baby. I’m not here to be mom shamed, I’m just looking for a little advice on how to make tummy time a little easier for my little one. I do know how important tummy time is but we’re having a little trouble with it. Since my son was born I’ve laid him on his belly on my chest, but after getting home from the hospital I had a little bit of a tough time healing and really couldn’t get on the floor with him to do tummy time, but every day I would lay him on my chest. When I started to feel better I did start tummy time on the floor and he’s always absolutely hated it. He burrys his face into the floor and instead of lifting his head and upper body he lifts his legs. He’ll be 2 months on November 3rd and is still only lifting his legs when he’s on the floor. I’ve tried putting him on a boppy and he cries and just lays there, I’ve tried supporting him with a rolled up swaddle blanket while he’s on the floor and that doesn’t work either. When he’s on my chest though he pushes up on his arms for a few seconds and lifts his head and looks around, he can also hold his head up without being supported fairly well, just not for very long. I really am trying but I’m not okay with just letting him smash his face on the floor and scream. Does anyone have any suggestions or ideas? I’m worried he won’t develop the way he’s supposed to.