I'm not a geologist, but 2000 m in 37 million years is ~0.05 millimeters per year. Is that about the right rate of growth for mountains formed through subduction and volcanism?
By comparison, the Himalaya (maximum height, > 8800m) are only ~50m years old, are among the fastest rising mountains in the world, and Everest itself has an average growth rate over the period of 0.18mm/yr.
The fastest rising peak, presently, is Nanga Parbet, in Pakistan (part of the Himalayan Plateau), rising at 7mm/yr.
That's 70mm/decade, and 700mm (~3/4 meter) every century.
[Also not a geologist, but] apart from volcanism from subduction, there were also other landmasses being sheared off the subducting plate and accreted onto the western part of the continent. It was all probably higher before the many millions of years of erosion up until now?