Just caught a scaredy cat outside- need tips on socializing her.

Okay so I just caught a cat that was outside but she's so shy. She doesn't look that old, maybe six months old? so not a baby but still a kitten (of course, I'm no expert, she could be older and just really small) and I also don't know if she's a girl for sure, I'm just guessing on that for now too. Right now I have her in a small dog run in our garage to keep her away from my other cats and dog while I try and work with her. Basically I want any and all tips I can get. What can I do to help her thrive in her new environment? Besides love and patience, of course, those are a given. She's just so scared!

Also, how soon should I bring her to the vet? I'm just worried that I will traumatize her more, and I'm not sure if she would even let the vet get close... she's very scared! But I would like to find out more information on him/her, for starters, is she a bot or girl? Is she fixed? Could she be pregnant? Is she healthy? Those kinds of things.

She should go to a vet now. She should be vaccinated and dewormed. Thank you for taking her in!

Ferals and strays are often malnourished so will often look smaller and younger than they are.
I fed a stray that looked like a kitten and after less than 2 months of feeding looked like a 2 year old.

Smh well I have to catch her again. We had her in a small dog run/large dog kennel and she somehow escaped. I was completely mystified at first considering it's a six foot tall, metal cage with a cover on top. But the top is made of a tarp material so she climbed to the top and fit herself between that and the cage... impressive, I have to admit. But now I'm sad because I have to catch her all over again!

I helped a neighbour catch a feral.
The way I did it. Strong fishy smelling food. Opened it infront of cat. Put in bowl infront of cat. Put bowl inside hallway or back door. Sit by door avoiding eye contact. Wait for cat to gingerly enter. Wait for cat to eat. Quickly close door. Wrap cat in thick towel. Place in cat carrier or box. Done