You can make him a shelter- there are plenty of instructions online if you google, and how-to videos on Youtube. If you can spend the money, there are very nice outdoor cat shelters available on Amazon, from basic to elaborate. Some are practically palaces.
Do you know anyone in the shelters in your area? They might come and trap her and then spay and release. Or maybe it just a scared housepet they can rehab and find a home for her. It’s worth a shot.
As an aside: One of the strays around my mom’s house was scared of all humans, for her first two or three years. But she’s since gotten to the point where petting her is not an option. It’s mandatory. She will literally refuse to let you feed her until after she’s been petted.
So yes, it’s possible that you might win this cat’s trust. No guarantees, of course: You can never tell with cats, after all.
I have a cat carrier with the door missing (making it useless as a carrier) that I put out on our front porch just in case any of the local “strays” need shelter. Blanket in side, towel over the top for warmth. From time to time I see one in there.
Setting out food and water is good. Slowly moving the food toward the carrier might help him see it as a safe place. Good luck! Hopefully he comes to trust you.
I adopted one of the neighborhood strays this way. I put out food and water in a somewhat sheltered spot and kept them filled. After a time, I added a blanket next to some nearby bushes. I did put out a cat carrier, but he never went for that. I never figured out where he slept, but he did become my buddy. We had a daily chat (AKA pet session) and I took him in for shots and flea meds and such). He was a sweet guy.
We’ve trapped a few kittens that seemed feral and frightened, and they warmed right up in a few days. I think this feral versus friendly trait is something that is learned early in life and there’s some leeway in how early it has to start and how completely it works. YMMV.