Can you get into a top grad school coming from UT Knox? I went to the University of Tennessee at Chattanooga where I got a BA in Philosophy and graduated with a 3.4 GPA. During my senior year, I discovered an incessant love of physics. However, I’ve had to start over practically from the beginning, such as learning pre-calc.

I am now attending UT Knox for an undergrad physics degree. UT Knox is a public school ranked #83 in physics. My question is, how well do I need to do to come from a school like UT Knox, at my age, to be accepted into a top 10 graduate school? I know the odds are stacked against me, but I plan on overcoming them.
I think you are asking the wrong question. For the specific question, your chances of acceptance at a top ten graduate school are near zero. That has nothing to do with you or where you go to school. It is just numbers. The fraction of accepted candidates at such a small set of schools is minuscule. 

A better question, that I think will leave you more satisfied, is what you need to do to get into a really good school that will help you meet your overall life goals. It would be sad if at the end of your life the only thing one could say about you is "he went to a top ten grad school." 

The way to success to to work hard, learn a lot, read, write, emulate those you want to be like, be bold when necessary, ask for help, learn to work cooperatively, don't burn out, be flexible, practice, ....

You can do all of that anywhere. You can even do it while being a bit of a goofball. 

For the record, lots of people are late starters. I never had a positive educational experience until the second or third year of HS. My HS doesn't even exist anymore. But I learned how to be better and wound up with a doctorate and a successful academic career. 

But when it does come time to apply for grad school, apply to one or two top schools along with some others. There are a lot of good schools that will help you build a great career and life.