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How quickly can I form a mountain chain?

I'm designing a world, and I want it to have major geological changes over a short period of time. This includes continental drift, which I'm assuming should have some interesting results. In particular, I'd like to have mountains form, which in turn should change part of the world's climate (I'm guessing) by impacting wind patterns. However, while I'd like all of this to happen rather quickly, I don't know just how fast it can happen, as I don't know how fast continents may move and then collide.

Here are my parameters:

  • The planet is Earth-like, with the same sort of seasons.
  • There are four large continents, each about the size of Africa, spread across the globe.
  • I want the mountains to form quickly, ideally reaching heights of 30,000 feet within a few million years from the start of a collision. They'll probably keep going, but this is my target reference height.
  • The area where they'll form was previously mostly flat.
  • The whole chain should be roughly 1,000 miles long.

Is it possible for these mountains to form in about a million years? If so, can they form faster? If not, how much longer would it take?