And if you are really pressed for short term gain, why not simply stay in despotism?
Because you can't irrigate for more food on grassland tiles without a food bonus in despotism. Feudalism can yield more food, and that food could turn into units for conquering The Great Library.
But is it really a smart strategy?
For sure, no. If you're behind in technology that the Great Library elevator makes sense, then the better strategy consists of the following:
1. Only have one roaded tile in the 8 adjacent tiles to your capital (or only one on your borders). Also, no harbors if you have a coastal capital.
2. Get some lump sum of gold.
3. Get a trade network with your neighbors.
4. So you can trade for a luxury or resource? Then loan out your lump sums of gold for any AI gpt at the maximum rate. At least aggressive, that's 1 gpt for 18 gold.
5. Then come back to the same AI and pay gpt for the luxury + gold + any technologies (and later maps) from the AI(s).
6. Then cut your sole road next to your capital.
7. Then re-road that tile.
8. Finally, reacquire all luxuries and/or resources you can get with gold per turn, so that on the next turn you can:
0. Pillage the road and start again on getting any gold, gpt, or technology that the AI(s) with a luxury or resource have.
Then there's likely no need for the Great Library, and one can get the AIs gold and gold flow for buying improvements and upgrading units.
Instead of aiming to capture the Great Library you could take territory that betters suits your economy and thereby increase your net commerce to buy cheap techs at a rate higher than 1 tech every 4 turns.
Is stealing technologies via the espionage screen (which doesn't require The Intelligence Agency, only Writing and an embassy) less expensive than buying a technology? This does vary somewhat. I think sometimes buying a technology is less expensive, and sometimes stealing is less expensive.