Well, you needed the means to get an education, since most of the poor in those days were illiterate, which is something of an impediment to becoming a successful writer.

I can only think of one writer off hand who wasn’t a wealthy landowner, although it is a particularly notable example; that of William Shakespeare.

Shakespeare wasn’t poor (his parents seem to be of upper middle class standing), he was able to get a basic (but not a university) education and then pursue an acting career (with perhaps a side hustle as a teacher). Whatever the case he certainly wasn’t independently wealthy before he started writing, he needed to earn a living.

He did seem to be in it for the money (and fame) since he wasn’t just a writer he was an actor, theatre owner, and something of a celebrity, and he did make enough money to become a wealthy landowner by the time he died.