Do I still have a chance at top tiers?

Hey all, I’m facing a dilemma and I need some insight.
A little background info: I went to a middle school that had very little to offer in the way of advanced courses. I moved after 8th grade to start high school at a far more rigorous establishment. However, since I had gone to such a crappy middle school I had to take low level classes in my freshman year (algebra 1, earth science, etc.) and sophomore year (geometry, regents bio) alongside multiple independent studies in order to catch up to the honors track. My only impressive class in sophomore year was AP world, which I 5d.

My junior year was, I believe, quite competitive. AP physics 1 & 2, ap micro, APUSH, ap English, precalc and some requirements. I also joined a ton of extracurrics and clubs during junior year, got elected president of the student association, and was selected to work at the physics lab over the summer as part of a research project. I also got 5s on all my APs.

While my junior year was perhaps indicative of my potential, I’m very concerned that my first two years playing catch-up will weigh me down enough to keep me from getting into top schools, e.g. Cornell and Carnegie. Does anyone have any thoughts on how colleges will look at my trajectory, and whether or not I should apply to ivies and such?

If it helps, some stats: I’ve consistently held a 3.85-4.0 gpa UW all 3 years, have all 5s on ap exams
Extracurrics: Scioly, SA, MUN, key club, green team, physics research, volunteering at a senior home, soup kitchen, school improvement planning committee, tech committee, chess club, cross country

Also not sure if it matters, but next year’s schedule is AP comp sci A, AP psych, Calc II, AP Chem, public speaking, film lit, AP us gov, and some stuff I’m forgetting

Do you have AP stats (did you take the test for all the AP classes you were enrolled in?), current gpa, SAT/ACT, Subjec tests?

Colleges, at least the high tier ones, don’t really care about AP tests at all. Which makes us need your SAT II, SAT< ACT scores to be able to give you any chancing.

Chance me back? http://talk.collegeconfidential.com/what-my-chances/1903603-harvard-and-mit-chances-any-advice-welcome.html#latest

Why do you want to go to a top tier school?