"Is international research contests and mathematical olympiad can give me a big chance? "
Unfortunately, not nearly as big a chance as having perfect stats accompanied by a donation of tens of millions of dollars.
Assuming that isn’t going to happen, you’ll have the best chance of you are one of the top five or so students in your country. Harvard’s acceptance rate is 5% but that rate for international students at Harvard, the ivies, or any top 20 university drops to only about 1-2%.
Apply by all means! You certainly can’t get in if you don’t try. What everyone is trying to tell you here is that it would be a mistake to rest any of your hopes, dreams and future plans on any top 20 university in America. College is a step, part of the journey. It is NOT the destination. If you think you are smart enough to have a chance at the best schools, you are smart enough to understand the odds and form backup plans that also excite you, and will prepare you well for life BEYOND college.