My girlfriend and I were trying to remember where Latvia was in Europe. After opening Google Earth, I saw it was next to Estonia, and Lithuania. Then just south of there, beneath Poland, is Czechia, Slovakia, Slovenia, Austria, Croatia, Bosnia, Serbia, Macedonia, then east toward Romania, and Georgia.
Then I remembered old/local names for places, like Italia, Germania, Brittania, Francia. Even though it doesn't have the literal suffix, "-ia," this could include España. Even in the US, there's Pennsylvania, and another Georgia.
I assume it goes back to Greek or Roman, judging by the areas, and probably meant something along the lines of, "land," "of the land," "realm," etc. But I found it hard to Google and search for this exact question.
Where does this suffix originate, and how did it come to be so prevalent among so many different cultures?
-ia is a Latin suffix meaning both "land of" and indicating a group of things. The suffix came to Latin (and then English) from Greek, and to Greek from Proto-Indo-European. It also appears in Slavic languages as -ja or sometimes -a ("Srbija", "Makedonija", "Hrvatska").
You'll notice that in countries with Latin-derived or Indo-European-derived languages, the suffix is usually included in the country name (Romania - Romanian being a Latin-based language, Shqiperia - Albanian being an Indo-European language, etc.) This isn't the case for a few of the countries you've listed in their native language, such as Georgia ("Sakartvelo" in Georgian, a Kartvelian language) and Austria ("Österreich" in German, which is an Indo-European language but forms its own Germanic language family as well and didn't keep this suffix).