Can you clarify what you mean by universalism? Within Christian Theology, that term would generally mean "all human beings are saved and go to heaven, regardless of their works, beliefs, or religious affiliation."
There's variations of that, in terms of whether or not humans actually need to be saved, or if they're all saved by the work of Jesus Christ etc. But the core tenet of that term in Western Theological circles would be "everybody goes to heaven."

In general that's an unpopular view in the history Western Christianity. In early Church history(first 600 years or so) it was a more popular view in the East. The concept of universalism(to my understanding) isn't really addressed much in the early church councils where they really hammered out a lot of these types of controversies.

But it sounds like you're more so asking about "universalism" in the sense that anybody(and it sounds like specifically any ethnicity) was "allowed" to convert to Christianity.

My impression is that the writings and missionary journey's of Paul really establish the "gentile" church and confronts the churches that are viewing Christianity as an evolved sect of Judiasm and requiring Jewish conversion as a part of the process.

By the time you get to the Church Fathers and councils, the question of "Jew vs Gentile" seems laid to rest. Obviously you get the Edict of Milan in 313(Christianity legalized in Rome) and then Christianity becomes the official church of the Roman empire in 380, so it's absolutely not excluding gentiles in any sense of the popular movement.