For what it's worth, I saved my first $10k back when I was making $34k/yr. It took about two years of living cheap (in Portland, which is around the average in terms of cost of living for the US).

Doing this was my absolute number one priority from the moment I landed my first job after university. As it should be for everybody.

Once you have that stack in place, you can think about moving off of "college student scrounge mode" and into a world where you might consider owning a new-ish car, television, moving to non-shared housing or an area without crazy hobos camping on your doorstep, etc.