I don’t want him to mistrust me, so I guess I need to find someone like that group you mentioned and give a donation to their work.
He’s young, maybe 6 months, so hopefully he can be tamed. I’ll try anyway.
If the cat is hungry it will eat while you are still out in the yard.
I found that it was important to let the cat come to me rather than try to pet the cat. You might try singing to her. They like that. Don’t whistle though. Many cats do not like the sound of a whistle - even a very soft whistle.
So let the cat come to up and bump up against you. If you try to pet her, try just petting the tail first. (It’s furthest from the front claws.) Once she’s okay with you petting her tail then pet the top of her back near the tail.
You definitely need to get the cat fixed. You don’t want a litter or your back yard sprayed. If you google Friends of Feral Felines and your city you should be able to find a group that will let you borrow a cage. It’s probably good to have a stranger handle the cage so the cat doesn’t associate you with the process.