You can google it. There are many sites which list math tests in your area and how they are taken. Some schools give some of the basic ones in school. But usually if you are interested you have to know which take place and the dates. It’s easier if your son belongs to a math club or group. Some math programs like Russian math also provide these tests. Some of the tests will give the first and second level online then the kids come in for additional tests. Some are teams with competitions. There are also events where kids come together like math prize for girls. There are also math circles in some cities. These tend to be run by parents or teachers and can be very high level or just kids who love math coming together.
https://www.thekidstory.com/math-contests-for-gifted-students/
Once/if he gets really interested there will be more competitions for him to look at. Some kids are really good in a specific area and others focus on a single test. It’s an entire world not unlike sports with a language and competitions. You will end up seeing the same kids. Mathcounts or Math kangaroo are probably good places to start as they are easier than many others. He can then get a sense of what he want to study.