We're currently in the information age, which is due to silicon. In a few hundred years, this time may reasonably be called the silicon age. Society has only recently transferred to the silicon age from the previous iron age. If we don't cause a total collapse of our society, then we will be in the silicon age for a few hundred more years, and that will likely include space colonization.

The space age you're referring to is likely the 60s, when space exploration was beginning. A decade or two isn't long enough to be considered an age.