Building the Great Library or not?

I've played Emperor Culture games a few times now, and I saw the GL gets made at T39 twice. So yeah uh, GL isn't necessary for Culture wins at all. Though I don't know if I'm being optimal, but I've managed to secure victories in my last culture game as Brazil around T260~ ish. GL is not worth the granary + library + archer you can build in the mean time. Besides, the early slot is irrelevant considering the bonus don't pick up until around the Industrial era (when you actually discovered all the civs).

I found it useful to build GL as Venice in order to get to Iron Working and ensure that I had the Colossus and the extra trade route with it.

If I try to build the GL I get destroyed by my neighbors

Well, if you're going to be an early-game wonder-builder, the GL is a great one to go for. Free tech, bonus science, earliest possible generation of GS points (often overlooked benefit there), and even a nice slot for you to drop a book off in after-hours.

But you'll want Aristocracy sopol and/or Monuments to the Gods pantheon, or some other edge (that first golden age is nice, so is marble), as it's not only in demand, but you don't need to waste too much time on this.