is it impossible to become ivy league professor?

Answer 1

In order to become an Ivy League professor you need to get a PhD from a top school, write a dissertation that is likely to get published in the top journal in your field, have the potential to publish lots more articles in the top fields. In addition, the Ivy League school has to have an opening.

If they have an opening, then they will interview about 30 prospects like you. They will invite between five and ten to come give a talk at their school and then make an offer.

Failing this process, you can go to another school. If you turn out to be a star, an Ivy League school may try to hire you away.

If you fail to do this, it is possible to get a one or two year visiting position at an Ivy League school (I had visiting positions at MIT and Wharton right after getting my PhD -- so know it is possible).

Answer 2

Obviously, it's not impossible, as individuals are Ivy League professors--although, I'd almost be willing to bet that that was not the first paying position in their lives. That would be a long-term goal in your life--set up some short-term, and intermediate-term goals as well.