It sounds like you are on a great start! Wish I had discovered MMM when I was 18.
I come from a fairly frugal family (relatively), at least certainly they were very much that way when I was growing up. I was pretty impoverished as a teenager and young adult going through uni, I had to be incredibly stingey, not by choice all the time.
One thing that is super common though, even amongst stingey uni students (I am a young Uni employee now at 32 so see this a lot), is that people go through an impoverished phase through Uni. They are often quite good at getting by on not too much. Then they graduate, get full-time jobs, etc. Their salary increases. But they end up not saving much more. They don't notice it, but their lifestyle inflates in all sorts of ways to consume that new income. Its not necessarily intentional; it wasn't for me. But I noticed it after a while. It can be really hard not to inflate your spending with new income, especially when you've had to be so careful as a student, and often go without stuff that you shouldn't eg healthcare, fixing your car, etc. Some things you should inflate for. But be conscious that this is an easy mental trap that people fall into, even the most frugal ones. I think awareness of this phenomenon will make a huge difference in how much you can save. I think you can train for it now, also. You might not be able to save much perhaps, but perhaps you can save 5%, or 10%. Excellent. Do it. Let yourself have an emergency fund (I think this is a time when its ok to have one, eg you don't have a Credit Card or Mortagage offset to use as an emergency fund, reliable job that you know will reduce your risks, etc) of a couple of grand or so first, then, index fund away.
The benefit of the few percent saved in index funds won't make much difference perhaps on your FI date in itself. But I think the lessons learned, the extra tightness on yourself now, the learning about the funds, tax, managing them, etc, will be FAR more valuable.
Like I said I wish I had discovered this stuff 14 years ago at 18. The above is what I would have done. I've given some of that advice lately to some postgrads that care to listen, I'll give it again and again.
Comp Sci/Programming... I'm sure you'll have fun using your skills to help you manage your Moustachianism :-)
Also, excellent field to get into for FI. Plenty of threads on this, but, lots of programmers out there semi-retire early, or live overseas in cheap places (increasing their savings rates) working remotely on contracts etc. Its a good field for that. Plenty of seasoned hands on MMM and indeed other places online that have done that to learn from :-)
Best of luck!