Did apartments exist in 1902?

You could look up the word in historical documents through google ngram, and the etymology is oft dated.

In this case, "apartment" shows up a lot since at least 1750, and the word is allegedly from the 1640s, french, meaning separated room(s) for an individual or family.

Of course, in practice those may have seemed hovels compared to the modern lifestyle.

Tldr yes.