As others have said, to be very well prepared to study mechanical engineering your best bet is to do very, very well in your math classes, and also in physics. The point is not necessarily to jump ahead in math. Instead you want to do very well.
Some top schools in the US (Harvard, MIT, Stanford come to mind) do not admit by major. However, for these schools you are better off to do well in essentially everything, and doing particularly well in classes that relate to your likely preferred major is still important.
For an international student, for the really top ranked schools in the USA, being quite close to the top student in your high school is a good goal, if not close to the top student in your country (perhaps top 10 or 20 for a large country).
There are a lot of universities in the US that are very good for mechanical engineering. Anything that is ABET accredited would be good. You do not need to attend an “Ivy League” school.
Also, for a potential engineering major, being precise is a good plan. To be precise, the “Ivy League” is a group of 8 specific universities. They are all very good. However, the top schools for mechanical engineering (such as MIT, Stanford, Georgia Tech, UC Berkeley, U.Michigan, Purdue, Caltech, …) are mostly not in the Ivy League. However, Ivy League schools do have good need based financial aid and some of them are good (and ABET accredited) for mechanical engineering. Ivy League schools are also generally quite difficult for admissions for an international student, as are the top engineering schools in the US.
People who hire mechanical engineers, at least in my experience, know which universities are best for mechanical engineering.
Also, being a mechanical engineering student at a top ranked university is not going to be easy.
Being a mechanical engineer can be a very good career, but I have never heard that it is easy.
All of this leads to two questions:
What is your budget? Can you afford to be full pay at an expensive university in the US (at perhaps $80,000 per year or more)?
What do you mean by “Ivy League”? Do you mean “highly ranked US university”, or do you mean “the 8 well known and very good universities that compete in the sports league known as the Ivy League”?