Applying to MIT in this situation is like buying a lottery ticket - go for it if you want, but assume it won’t happen, because realistically it won’t.
Getting actual need-based aid is a long shot in this situation, for all the reasons others have described. And the longer-term question of how you’re supposed to make the leap to legal status and be able to gain employment here once you have a degree is a very significant one as well.
You’re in a tough spot that isn’t of your own making. It isn’t that you can’t get an education here while undocumented. There are schools you could probably pay for with off-the-grid income. This article, for example, lists several MA public U’s with very affordable sticker prices for internationals; and you might even be able to get some merit scholarships to reduce the cost further. https://www.usnews.com/education/best-colleges/slideshows/15-most-affordable-colleges-for-international-students?onepage
But if you don’t start this process from outside the US, and get a legitimate student visa to be here and pursue your degree, then what happens after that? You’ll have a degree that proves you were here illegally in order to earn it, and that will throw up an additional barrier to getting onto a citizenship path as you hope to do. I’m not an immigration expert, but I don’t see how this serves your goals. A Canadian degree obtained with student-visa status would be better than that, as would a degree from a university in India or Europe or wherever you can legally be a student. Now, if you can afford to attend a college here based on full-pay minus merit, and you can get a student visa to do so, then that’s different. Even starting at Bunker Hill on that basis could get you a foot in the door. Make sure you get good advice at this stage and don’t end up digging yourself deeper into a hole that will make naturalization impossible in your future.