Welcome Michael, and congrats on your new piggie! She's precious!
Resistance to being picked up and/or held -- including running away, going stiff or limp, or crying out -- is all normal behavior for a guinea pig. Unlike dogs which are predators like us and see us as being members of their pack, guinea pigs are prey animals and only ever see us as predators. They don't really become "dominant" with humans. They're just scared until they've become used to humans enough that they know we're not going to eat them and in fact, we are more likely to feed them.
It takes a lot of time and patience to earn a guinea pig's trust and a lot of hands-on positive interaction. A good place to start is by feeding your pig veggies or treats from your hands; this helps them associate your hands with good things. Catching them can be difficult, especially in a large cage, but once you've caught them, try sitting down with the pig on your lap and feeding them some veggies. Some pigs will never really learn to like being held, but with a lot of gentle handling, patience, and positive reinforcement, most of them can at least be caught and picked up without excessive stress.
Here's a link that has a ton of useful information for new pig owners:
https://www.guineapigcages.com/forum/threads/113176-Information-for-new-guinea-pig-owners
Everyone on this forum is very nice, and there are a lot of experienced pig owners here who are happy to help answer questions. We're glad to have you here!