Realistically, they can't and won't unless it's a very large scale that's worth pursuing, for a multi-national corporation with enough money to pay a big fine. If a company is not doing business in the EU, not selling into the EU, they can of course entirely ignore the GDPR.
In the case of a large company that sells into the EU, and refuses to obey GDPR, what you'd likely see is the EU pursuing that company on its domestic turf legally. A company out of NYC for example could be pursued in a court there for fines related to GDPR violations. The larger those violations, the more likely it'd be pursued by the EU across the Atlantic. This is how it works already, there's a lot of international business precedence. The stronger the legal system in the home country you're pursuing the multi-national into, the better for the EU's case.
If I set up a business in Germany, dump large amounts of toxic waste and cause very costly environmental damage, and then (somehow) quickly flee the country leaving no assets or business behind - but back in NYC my company has vast assets, you'd find the company pursued from Germany to its home in NYC for those damages. They still have to win the case of course.
The EU fortunately wasn't dumb enough to attempt a global claim on regulating privacy. They pushed the line pretty far, but did not cross their own boundaries. I think they fully understood there was no scenario where the US and China (40% of the global economy) - or frankly most nations - were going to care about EU law projections external its jurisdiction.