Yes, and globally that's still nothing. You are talking about the elite of the elite, chosen ones among the chosen ones. In other 1st world countries, and even in majority of USA no, recent graduates are not paid quarter of a million dollars. There's a select, very exclusive, very limited group of people who do. But like others have pointed out already - that's not "typical" by any definition of the word.
If you grew up in a shitty high school, you can go to a community college and then transfer to one of these state schools. I know for certain California has excellent policies that favor CC applicants transferring in. There are multiple ways in the door if you apply yourself.
Perhaps consider that a student that can't even get into a state school has no business or ability to write code at a level that would merit a 250k salary. The bar is on the floor.
Like I said, the software engineering job market is red hot right now. I rejected a few offers and they still asked me a few months later if I would be interested in joining. That’s how desperate they are for anyone with even a reasonable amount of talent.