You can (rarely!) get normal-sized Ancient Cores by flipping over dead Guardians
The most important part right at the start: "dead" Guardians are the ones that do not move at all. The ones that still shoot laser beams are called Decayed Guardians and they can not be flipped over. Killing a Stalker and flipping it over during the dying animation will not give you extra items either. This ONLY works with the ones that are already dead right from the start.
These are the drop tables, datamined from the game code so there was no trial and error involved - just raw data from the guts of the game. That stuff determines what enemies drop under certain circumstances.
If you search a dead Guardian, you have these drops:
RuinGuardian - x1
52.0% - Ancient Screw
25.0% - Ancient Spring
15.0% - Ancient Gear
8.0% - Ancient Shaft
Translation: You get ONE item and it will never be a core.
If you flip a dead Guardian, you'll have these drops:
FldObj_RuinGuardian_A_Dynamic
Normal - x2-4
22.0% - Ancient Gear
35.0% - Ancient Screw
26.0% - Ancient Spring
15.0% - Ancient Shaft
2.0% - Ancient Core
Translation: You get between 2 and 4 items and each of them has a 2% chance to be a normal-sized Ancient Core. It's random and rare, but it does happen - even if you haven't left the Great Plateau yet.
Question: Can you flip them all?
Not all of them. Most are stuck in the ground and won't move, and you can't flip the ones that still shoot laser beams - but if you find a "dead" one sitting on the ground, you can flip it over with either Cryonis (if there is water underneath it) or by pushing something heavy against it using Magnesis (like a treasure chest or a Boulder Breaker).
You can also topple them by stasis-launching something heavy against them, but it can be tricky to hit the correct spot for that. It is also a "one time only" type of deal: you can turn them over as many times as you want to, but they will only pop out loot the first time.
This is such a cool and unique fact of the game. I never even thought about doing this. By the end of the game I had so many screws that I just ignored the dead ones all together not knowing there were better possibilities.
Most of them can't, so it's not unusual to think that ;) for example, there are a couple dozen dead Guardians scattered across the Great Plateau, but only 3 of them can also be flipped (one near the Bomb Rune shrine, one near the flooded old entrance, and one near the Temple of Time)
if you search for FldObj_RuinGuardian you will see ALL of the dead Guardians.
The ones called FldObj_RuinGuardian_A_01 are the ones you can only search, but not topple over
The ones called FldObj_RuinGuardian_A_Dynamic are the ones you can search AND flip over for a bit of extra loot.
Keep in mind that the cores are still super rare, but if you're adamant about getting cores then you can just savescum (save the game, flip the Guardian, if the loot isn't to your liking then reload and try again until you get what you wanted)