The earliest was during the Mauryan Period. This is the age Dalrymple is talking about, the time of Aryabhatta, the popularization of Buddhism, arguably the time when most of the Indian epics were written (dating them has become notoriously political to the point that discerning the truth is hard now). This is the age Indian nationalists stress on, and the left wing tries to ignore. This age declines because the empire got too big, lost control and slowly disintegrated.
The second age was during the Islamic golden age for India which the right tries to ignore and left stress on. My general sense is that there was a golden age of architecture, poetry and arts and probably not so much in Science. The Taj Mahal for instance was built during this time. This age declined mostly due to wars, the Mughal rulers were never successful in fully unifying India, even to the extent the Mauryans did. They fought consistent wars against pockets of resistance in the South, and towards the end began losing these wildly expensive wars (leading to a brief reign by Shivaji)
The third golden age which no one wants to admit (left or right) is the British Golden age. There really was a renaissance in Indian thought in arts, science during British rule. This was when Indian history was “rediscovered”, first by British orientalists and then by mostly Indian Bengalis. CV Raman won the Nobel prize in science, Tagore won the Nobel prize in literature, Ramanujan etc, the names are numerous. The British rule also was the largest and most stable unification of India till the modern times. After 1850s there were almost no pockets of military resistance against the British rule. The British age declined with WW1 and WW2, and ended with Indian independence.
Post independence was not a smooth going party. If you came to India during 1980s, you could argue independence had been a disaster with everything getting worse post independence. But since 1990s economic liberalization India has a new ish golden age with unique characteristics. Who knows how long this will continue and when it will inevitably end