I don't know what academic major I'm fit for. So I have a solution. Is it the right solution though?

Once upon a time, it made sense to take a couple of years of college to figure out what you wanted to do, or to make yourself a well rounded individual with good critical thinking skills. This is now a luxury that few can afford.

How in the world does that work out when College Algebra is a prerequisite for Calculus I? Did every engineer just have to test out of Algebra?

I honestly didn’t see what you said at all. I was told that the music major was unusual in requiring classes in the first semester. I also know quite a few people who transferred in from a community college, where they took their gen ed requirements while they discovered what they wanted to do.

And unless you have something you know you want to do that doesn’t require a college education (and still likely won’t in the future, as that’s becoming more and more a requirement), I definitely wouldn’t recommend forgoing college entirely. Even an associates degree gets you a leg up in many fields.

If you need to take algebra in college, it’s very unlikely that you are cut out for an engineering degree.

That’s pretty much true. I even got a semester credit for the Calc I took in high school. If you don’t come in able to take Calc, you’re behind.