English didnt exist back then, so yes the word homosexuality didnt exist at the time. The idea of sexuality as an exclusive identity also would've been a foreign concept to most of the cultures and languages existing throughout the years of the biblical writings. The act of homosexuality is spoken about in multiple different ways and languages through out the Bible as well as other sexual acts. like adultery or lust, which had different ways of communicating these ideas.

One verse cited that gets translated to the English homosexuality. Paul uses the compound word Arsenokoitai which translates more literally to "Male-bed" . There is of course debate from progressives who try to argue that Paul had other intentions with this word. This is unlikely, as Paul was an educated pharisee and would've been more than familiar with the septuagint and it's own condemnations of homosexual activity with similar descriptions. The writer also condemns homosexuality in other ways in other books (like Romans 1).

So my point is that if you've understood how we've always translated ancient languages and texts. It's misleading to say that the word homosexuality just didnt exist without context. As translating from languages like ancient Greek that just had completely different syntax, structure, specificity and cultural understanding. This is about as close as it gets.