An infant from 300k years ago, if brought to modern times, should grow up and be capable of everything modern humans are.
Great point. I like to consider birds for questions like this one.
Bird brains come in a relatively set range of sizes, but in a wider range of skills[^1], and hominids living in earlier times may have definitely needed different skills. Birds have had many millions of years to evolve. To remain flying they needed to keep their bodies small, nimble and light and they can't grow larger heads, so evolution works within those constraints. Now, there are generalists among birds, and even tool users, but who knows how long it took them to evolve their "3 nanometer process."
On the other hand, hominid's brains are very plastic, which can be due to evolution saving on "design optimization time" (and we haven't been around for as many millions of years as birds). A figurative way to explain it is this: to fish at the local pond, it's more economical to buy two general purpose computers ("have more general-purpose thinking matter") and to pay for their upkeep than to design a new computer from scratch. Later, if you decide to live from honey-farming, your computing could be used for that as well. You may need an order of magnitude or two more fish or honey to pay for your higher mental elasticity running in a sub-optimal "300 nanometer process", but it's a small price to pay for not being hostage to a fixed ecological niche.
So, I bet that humans that had made it in a short period of time from Africa to a different continent where highly adaptable, and they could probably understand most things we do today.
[^1]: https://phys.org/news/2018-07-neuroscientists-uncover-secret...
The history of anthropology is full of pushing events back as we improve our methods.
Europe is mostly believed to have been settled via Africa, the Middle East, and Western Asia. https://en.wikipedia.org/wiki/Genetic_history_of_Europe
(I am absolutely amazed by all the various humanity and technology origins. It's almost as if there is a direct path from the first person who used teeth and fingernails to pry a rock and fiber to make a spear to kill an animal and use its bones to make high quality tools for knapping stone, all the way to the lathe, which was the tool that bootstrapped the industrial revolution).
the cannon boring machine was what enabled the efficient steam engines which unlocked large mechanical shops (along with high quality cannons), while the lathe enabled precision machine tool making. I am sure many things had to happen around the same time for the revolution but IMHO the lathe was the true linchpin