To be honest, it depends. My high school and the surrounding school district area is extremely competitive with a great emphasis placed on grades, extracurriculars, etc (I’m a Northern Virginia kid). Generally speaking, my friends and those around me took all honors classes as a bare minimum and by the time we were seniors, we were taking dual enrollment classes in math, having maxed out of high school level math. HOWEVER, this is not the same for everybody. Not only are individuals different, schools are as well. There’s a vast variety of schools in the US and when you apply for colleges, admissions will receive a sort of info slip about your high school with explanations for things such as grade averages, special education systems, etc.
It seems like your a pretty high level student who aims to get into a good college, so I’ll speak to you as if I’m giving advice to someone similar to my high school path. Taking Algebra 1 in freshman year will be disadvantageous. The standard student at my high school - in order to be considered competitive to schools like Ivy Leagues - you should want to aim to be taking an AP Calculus course by senior year. That being said, although colleges like seeing a standard for the courses you take in high school, your course load (as long as you demonstrate consistent or improving grades and the ability to handle higher level courses) matters significantly less in comparison to your personality, your interest in the school, your essays, extracurriculars, etc. Keep in mind that admission officers are people too and they’re looking to see if you would be a good fit at their college with a large emphasis simply placed on who you are.
Again, I grew up in a competitive area where A’s, 4.0 GPAs, and AP classes were the standard so my experiences will be radically different from others.
There are also other options you can explore. Does Troy offer summer classes for high school credit? If yes, you can take classes over the summer to get ahead on your math track if you are that worried. If Troy does allow you to do this, I recommend taking Geometry over the summer. From my experience, the class is a joke and the only thing you need to take away from it is trigonometry, which is taught to you again in higher math classes anyway. Granted, this will likely cost money so be prepared to spend if you can! Also, if this doesn’t work out, you choose to go to Troy, and by senior year you’re still worried about having only gone up to pre-calculus, talk about in your applications! Common-APP, your main platform for applying to colleges, offers a separate section at the end where you can talk about any concerns or explain anything that you believe needs clarification.
All in all, I hope you relax and take a deep breath. Either way, I believe that you will do just fine. Good luck!