How did this character survive being bashed on the head?

This answer, admittedly, lacks expert medical knowledge or extensive sourcing.

1. The human skull is a lot tougher than movies and television give it credit for. Shows like the Walking Dead depict people casually plunging knives into skulls, both rotten and freshly dead, with virtually no resistance. But bone is a very tough material, and the average human skull is more than half a centimeter thick. Piercing it would take a powerful blow with a heavy blade, like a sword or machete, not likely a small knife. Also, blood pouring from a head wound does not necessarily mean a damaged skull. The scalp has a lot of blood vessels in it, so any significant damage to it can bleed profusely, as did Ki Woo.
2. A fractured skull does not necessarily mean brain damage, and brain damage does not necessarily mean death. Many people have received much more significant trauma to the brain from gunshots and survived, such as former U.S. House Representative Gabby Giffords. It mostly depends on what area of the brain has been affected, and to what extent.

From livescience.com:

A person's chances of surviving such a trauma to the brain depend on the areas of the brain that are struck, the velocity of the bullet and whether the bullet exits the brain, said Dr. Keith Black, chairman of neurosurgery at Cedars-Sinai Medical Center in Los Angeles.

I'm not sure if this is a canon explanation, but the scholar's rock was hollow, a fake.

When Min-Hyuk gifted the family the rock, he described it as bringing material fortune, and for half the film, it appeared to. The flood scene was a reality call that devastated the Kims; all their perceived fortune had been an illusion. They pretended that they lived in the Park's house, but the sewage-flooded half-basement was their real home. Remember the rock floating in the sewage? A solid rock with no air pockets could not have floated. The weight could have all been in their mind.

The hollow rock being a metaphor for false hope is also consistent with the giver, Min-Hyuk, having ulterior motives. When alone with Ki-Woo, he quickly abandons his respect of scholar's rock collection and admits it was a silly excuse to get in touch with them, particularly Ki-Woo. To convince Ki-Woo to do him the big favor, Min-Hyuk dubiously praises his education and trustworthiness compared to his college friends. When he says all his peers in college were sexually starved engineering students, he actually lets slip his true intention: he feared that his crush could be taken by someone else while he was overseas. Ki-Woo, a poor high school graduate with no prospects, was not such a threat. No matter what Ki-Woo plans, he couldn't fake his way into a real career nor could he hide his family's identities forever from the Parks.

Now, that all sounds great, but as far as I know, this is just an audience interpretation that is going around. Nobody involved with the project had confirmed this. The closest I've read is the director deciding the rock should float spontaneously, contrary to their plan in the script. I speculate they had originally planned for the rock to sink because of the wider use of elevation as a metaphor for class; the rock sinking instead could easily indicate the Kims' awareness of their class.