Initially we had A.D., Anno Domini, Latin for Year of the Lord.
No one really had a use for “Before the Year of the Lord” until historiography took off as a subject of study after the eighteenth century (which is why, in English, B.C. (Before Christ) was written using English abbreviation.
Archaeology took off as a science at the end of the Nineteenth Century and a method of dating forward and backward from a fixed date became more important. Originally, the dating used was the handy (to speakers of English) labels A.D. and B.C.
While English has taken over as the “common tongue” for a lot of international research, it was fairly clear that a dating system named for the Christian Lord was not appropriate for works that included Jews, Muslims, Hindus, and lots of other people who did not believe Jesus was God.
The primacy of European and American support for these efforts indicated that we would use the same basic calendar in use in Europe and America for dating, but rather than insist on the religious names for the dates, they were re-cast as Common Era and Before (the) Common Era (B.C. and B.C.E.)
(Despite the musings of Science Fiction authors, the use of 1945 as the new “Year zero” for the Atomic Age and Pre-Atomic Age has never come to pass.)
B.C.E. and C.E. are not really new, but they have been getting more publicity as mainstream media catches up to the terminology used in science.
As to non-European societies, they tended to date forward from some significant event (the creation of the world, the establishmnet of some dynasty), just as the Christians did before archaeology and historiography became prominent. (Remember, we originally only had A.D. Jews are currently reckoning year 5761 (from Creation), Muslims are in year 1421 (from the Haj).