Your core gets stronger doing heavy squats and getting progressingly stronger on them.
I’ve seen a guy in the gym who’s improved his squat a lot and get under the bar with 315 to 405, doing sets with no problem in his balance/stability at all.
I’ve also seen a guy with pretty strong legs naturally, make tons of progress on leg press, and after a short time squatting, his waist seems to be shaking under the bar when he tries to squat.