In theory, every country that claims jurisdiction has jurisdiction. In practice, countries usually don't claim jurisdiction over things that are not their business, and judgements against you may be hard or impossible to enforce, and extradition may be hard or impossible to achieve.
As an example, if your site defrauded gamblers in Germany, then Germany would claim jurisdiction (no matter where the servers are, because in German law, a crime happens where it has its effect). Whether they would be able to do anything about it is a different question.
If the USA finds out that Americans and especially underage Americans are gambling on your site, then they can close down servers in the USA. They can ask for extradition but most likely without access. And they can arrest you if you ever touch US ground.
Everywhere's laws apply, if you host in NY, the domain is registered with a company in CA, you have a bank account in Canada, you have a users in TX, france and china, you are in mexico. They all apply. The law decides where the law applies, and the law usually says it applies "here"
In 2000 Yahoo! had a case brought to the french court due to selling Nazi memorabilia, which is illegal in France. The french court said you must stop allowing people in France to buy Nazi items, yahoo turned to the courts in California asking them to say that it was unconstitutional (1st amendment) but they said it wasn't as the french court was not effecting any US citizens, only the behavior of a US company when "in France". For more details see https://en.wikipedia.org/wiki/LICRA_v._Yahoo!
If your goal is to avoid any sort of suit or prosecution, you would want to keep everything in and perform all your business activities in Mexico. As soon as those servers go up in the U.S., a U.S. court would arguably be able to exercise personal jurisdiction over your business. This includes advertising in the USA or any other manner of “purposefully availing” yourself of the U.S. and the benefits derived from conducting business there.