As an American, you'd be far, far, far, far, far, far more likely to succeed in migrating by following one of the European countries' legal migration paths (each country has its own policies). Most European countries are very interested in allowing migration of skilled workers, and in several countries, being a fluent English speaker is a bonus.

On the other hand, it might be technically possible for you to meet one of these country's criteria for "refugee", "displaced person", "asylum seeker", etc. but it is _remarkably_ unlikely.