As Jay Helfert has noted, American pool was the only pool until the 1980's. A few had earned an important place in American pool earlier than that, with the most obvious being Cuba's Alfredo D'Oro, but foreign players were a very small part of the American pool scene until the 1980s.
The Filipino invasion is well known and well documented. The first time I saw a Filipino player compete live in America was Jose Parica at the 1978 PPPA World 14.1 Championship, but he did not have a high finish. The Filipino invasion was only getting started in the 1980's, and most of the Filipinos (Andam, Luat, Kiamko, Lining, Sambajon, et al) didn't come to America until the 1990s. The Filipino invasion continues today in full force.
The European invasion began, for the most part, in the late 1980's and the first European player to make a big splash in America was Oliver Ortmann, who won the US Open 14.1 title in 1989. Aside from the obvious example of Souquet, not many of the top Europeans came to America more than occasionally in the next years, and I'd suggest that Europeans in the American pool scene were few until about 1997, when Chamat, Lely and a couple of others began to frequent the American pool scene more than occasionally, with Feijen and Vandenberg following a few years later, and then, Hohmann and another German named Roschkowski. For the most part, though, the European presence in American pro events was minimal until about 2005, and it has been very substantial ever since. I think the WPA World 9-ball Championships in Cardiff, Wales in the first few years of the new millennium lit a spark for European pool,and European players have excelled for many years now.
I'm really struggling to remember which foreign women first hit the American pool scene, but the first foreign woman that I can remember making a big impression at an American pool tournament was Sweden's Ewa Mataya, who played here as early as 1981 in the World 14.1 Championship, and she was a major force in women's pro pool within a few years of that. There was also a capable player from Japan named Meiko Harada, who preceded Ewa, but was less successful.
To sum, Jose Parica, whose nickname in his PBT days was "the leader of the invasion" is deserving of that nickname. The leader of the European invasion is, without question, Oliver Ortmann. The rest is history.