My baby did this and I also found myself a single parent at 3 days old. I exclusively breastfed. I'll tell you what worked for me but I'll be honest that my health visitor would not have approved and she had me convinced I was going to smother my baby, so I was pretty terrified a lot of the time. However my midwife told me to do whatever worked for me, and that humans and the west in particular are the only people who expect a newborn baby, who knows nothing of the world and is likely born 3 months too soon, to sleep alone. It's not always realistic if your baby needs more time/reassurance.
Every time I wanted my baby to go to sleep I would first try 3 times to put him in his bassinet (later his next to me, when he was bigger). If that didn't work (which I'm afraid it didn't, for months), I then tried co-sleeping 3 times. If that didn't work, then I ensured there was absolutely nothing around me or him, and he slept on my chest. I would then sleep with him there like that. In all honesty, neither of us ever moved a muscle. A friend found similar, though her husband did not. Maybe something to do with the existing bond between mother and baby, I don't know. Either way, whilst I hated feeling like I was putting him at risk, I actually now don't think I did. I found we both slept well like that and because I always kept trying the other ways, he eventually did slowly get used to other ways of sleeping. Slowly, he would be happy to co-sleep part of the night, and then all of the night sometimes. Once he got used to that he'd then sometimes be ok with the next to me at the beginning, then co-sleep the rest of the night and only occasionally sleep on me. Eventually, he was happy in the next to me all of the time. I'll be honest, it took a few months to get to that point.
We got into a rhythm. He now sleeps in his own room as he's 15 months old and I actually look back on that time quite fondly. But I've had more sleep now!
Good luck, I hope you guys find a way that works for you.