That would be the ideal, but don't count on it happening unless you get EXTREMELY lucky, or somehow manage to fail upwards. (since internal promotion often has more to do with sucking up than skill or effectiveness)
Simply put, the majority of jobs people hire a "new software engineer" for can be done by... a new software engineer. A scrub straight out of college paid as little as the market will allow. WHY would any company keep you around long enough to qualify for better benefits, market sharing, or pay raises when they can just kick you to the curb and bring in another boot?
That's why MOST major software houses below the middle management level are little more than charnel houses, and why unless you go freelance or start a business (and why I HIGHLY recommend some business classes on top of your programming!) within 4 years of graduation MOST programmers end up flipping burgers, stocking shelves, mowing lawns, or saying "Hi, welcome to Walmart" for a living... like the vast majority of everyone else in this overeducated underskilled society with a degree.
You have to want it, you have to do it 500 times better than everyone else, you have to break through the ceiling into positions WAY above what you get fresh out of school, and you're going to get crapped on a LOT by society as a whole.
... to the point many of the most talented developers I've known the past 4 decades have either given up and walked away from the field entirely, or simply taken their own lives before they even reach the age of thirty.
In that way I'm growing sick of watching talented friends half my age pass before me.