How to get cores in Frostpunk 2
In Frostpunk 2 cores are difficult to come by. Unlike other resources such coal, oil, and food, you won't find core deposits within the borders of New London. Cores are components from machinery that predate the Great Frost, and they can't be manufactured: they can only be found.
If you played the original Frostpunk, you may remember that cores were important then, too (they were called "steam cores" in the first game.) They're the only resource that you can't create or produce yourself. Cores are extremely important in Frostpunk 2: they're components necessary to unlock advanced buildings and upgrade your city's generator. Here's how to find them.
How to get cores in Frostpunk 2
Cores can only be found by exploring the frostland. Early in your game while you're placing housing, extraction, and industrial districts, make sure you frostbreak your way out to the edge of your city map. There you'll find spots to place logistic districts. Each logistic district you build will give you frostland teams you can use to explore the map, and expanding the logistic districts and enhancing them with scout headquarters will add to the number of frostland teams you have.
Once you've got frostland teams you can begin exploring the map. Click a node outside your city and it'll bring up a little information about it, like what you can expect to find when you send an expedition there. Look closely and you'll see blue icons next to "Possible findings" which may show items like coal, prefabs, people, or cores. The core icon looks a bit like a lantern, and hovering your mouse over it will pop-up a tooltip that says "Cores."
Launch an expedition to that location, and when it arrives, look at the options (marked with "?") to see which spots contain cores. Cores are almost only found in small amounts: typically one or two, so make sure you give a lot of thought before spending them on advanced technology.
In Frostpunk 2's campaign, there is a location that contains more cores than you'll find elsewhere, but it will take quite a long while to reach it. In the meantime, be very careful not to waste the cores you find, and keep your frostland teams busy scouring the map for more.