There are a few ways people gain magic in my world:

1: worshipers of the island god, Verta, are often given fractions of his power. The greater his trust in you, the more magic he gives you. As the main conduit for magic to enter the world, Verta has a lot of followers who want his magic.

2: self taught. Some people have a natural higher affinity to magic. Everyone can use it, but people with more in their blood (like children from ancient magical families) are able to touch their own easier to learn to use it.

3: tattoo and shock. To see magic, you can either draw it to your eyes or have a azursteel (fictional magical metal) based tatoo drawn around your eyes, which allows you to see it. People without verta's blessing or the skill/power to learn it themselves can gain the tattoo to help them see it. But they don't have the connection needed to use it until another magic user shocks them with enough magic to establish the connection

4: near the death of a god. When Verta died, the explosion killed many, but those who didnt die were shocked hard enough - and exposed to enough divine magic - to gain the connectiom immediately.