Try positional therapy. There are a few devices that are like a little pillow that forces you to sleep on your side.

I was also diagnosed with mild sleep apnea (although I firmly believe it's a false positive because it doesn't align with my symptoms). Anyways, I also cannot sleep with a machine, so I bought this little pillow that you wear like a belt and it sits behind you and keeps you on your side.

There is also a dental/jaw device you can be fitted for that you can wear at night that keeps your jaw positioned so you can breathe.

I've also read on some oral exercises you can do to help with sleep apnea. The machine is absolutely not necessary for everyone, and there are other treatment options, although doctors don't seem to want to talk about them. I think they get paid to push the machine.