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The first perk in the one of the learning skill tree (Scientific) gincrease those numbers to 27% and 1.35% respectively, per each point of your characters Learning skill.
Also the more counties you have of a culture that already has that innovation, the faster you'll get it.
Increased development too.
There's also Exposure. This is an innovation the game chooses itself from the innovations neigbouring realms have. It only applies to 1 and gives you a +40% bonus towards it.
https://ck3.paradoxwikis.com/Innovation
The perk "scientific" adds 35% Cultural Fascination Progress
https://ck3.paradoxwikis.com/Lifestyle#Scholar
Also, the higher your learning skill, the faster the progress (+1% per level).
But only if you're the head of your culture.
https://ck3.paradoxwikis.com/Attributes#Skills
Another factor is the development level of a culture's counties.
The more they are developed, the faster the innovation progress.
https://ck3.paradoxwikis.com/Innovation
^
I don't play games with cheats lol. but when I beat this game numerously, then I played with cheats ofc, I used only fast construction cheat. its boring to wait. and cheating is also boring too xD
Btw I am giving him another information too and if you are noob play it on very easy or easy mode.