The latest I have ever seen GL go on Deity is Turn 34, and you can barely research Pottery and Writing in that time. You can get it with a high-production Immortal start, a Salty one or settling Marble or something. You can also chop it out on Immortal and if you get it done by the early 40's you're good.
Where the Great Library is broken is when you don't have to turbo it out and you can slingshot into Theology or Civil Service or something similar. Then you get an advantage on the AI that is hard for them to recover from.
Something I do when I feel completing it is in doubt is queue up a Library, build that to 1 Turn left then swap over to Great Library. That way I get failgold and failLibrary. But mostly I just don't even worry about Libraries, Great or otherwise until my cap is at least 6 pop. It's not worth the maintenance cost before then.