So one of the hardest questions for me early on in this game was actually a pretty simple one for most 4X games: how do you build up your science output early on, in the first 40 turns or so? Most of the big science explosion techs tend to come later: Scholarship is a very late tech, and Land Consolidation and Monasticism take a minute to get to as well. Even Metaphysics, the easiest of the science booster techs to access, is locked behind a section of the tech tree I often skipped in favor of others. So how do you go about getting enough Science in the early game to actually get to the techs that let you snowball? Well, thankfully the answer isn't too complicated.
The first is specialists! One reason it's important not to build too many settlers and overextend early on is because otherwise your early science can't grow well without specialists. The two early game urban specialists, which give +2 research at the Apprentice level, are found in Divination and Drama. Yes, these two techs are your early science boosters! They are the only early techs that give access to an urban specialist. Apart from these, making a bunch of rural specialists help too! This means that Administration for granaries is a science tech, and the Freedom law from Labor Force is a science tech, too because these both give growth, and more growth means more specialists!
To add to this, many families are great at creating specialists, too. Any family with a bonus to Civics helps get specialists trained faster, and the growth bonus from Landowners after making settlers and workers can start producing specialists for science, too! A Landowners city with a bunch of quarries is actually quite good for this due to the bonus civics from stonecutter specialists! But this means that Clerics, Landowners, Artisans, Patrons, Statesmen, of course Sages, and arguably Traders are all cities which can contribute well to science output!
Culture is an indirect form of early science, too. When your city reaches Developing, you can build up to two of the Odeon line of buildings, allowing you to get a second slot for another Poet and more science, then do it again at Strong culture. Once past the early game, these strong culture cities give access to other good buildings for specialists, too, but this guide is focused on the very early game.
The other more obvious way to boost early science is to make sure either your first ruler or heir have a good Wisdom output. Going Scholar, Schemer, or Tactician for your first character can be very strong, each for their own reasons but in no small part thanks to their bonus Wisdom directly improving your science output.
Apart from that, there are a few other things to look out for. Ancient ruins often have research events, sometimes events give a choice for bonus research, and sometimes you get the option of getting a court scholar. The Freedom (indirectly) and Centralization (directly) laws early on both boost science output as well. Then there are tons of little bonuses to look out for, such as Babylon's bonus to research for each city, or Hatti's global civics bonus which promotes faster specialist training.
Anyway, just wanted to put this out there because I struggled for a long time in the early game of Old World because the early research is a little less obvious to get going than the bigger research techs do. If anyone else has early science tips, would love to see them!