What non-European ancient civilizations colonized Europe?

The Phoenicians did. They were the first ones.

The Phoenician core lands are in what is today Lebanon, so they are clearly non-European.

Phoenician civilization (civilization as usually defined, shortly, as writing + cities + social stratification) developed during the Bronze Age, where they had strong connections with the Minoan and Mycenae culture. They rose to importance after the Bronze Age collapse, which they managed to survive, and into the early Iron Age, where they took over as the sole and main Mediterranean merchants. So, they fit into the “ancient” category, and we already checked the “civilization” box.

And while the main Phoenician trading routes ran along the African coastline, they established a number of settlements in Europe as well. Malta, Sicily (the most important one there being Panormos, which is today Palermo), Sardinia, and southern Spain - there, by far the most important one, would be Gadir, which is today Cadiz.

This map here shows Greek (in red) and Phoenician (in yellow) colonies:

Later, Carthage - as an offshoot of Phoenicia - would expand colonization mainly in again Sicily and Spain. These also were the areas where Phoenician culture was the most important for the cultural development of Europe (plus of course Greece, where there were very close contacts, but no colonies).

Source: https://qr.ae/psnU2q