From which age did the skeletal man belong to? How do you know?

The Quaternary Period; The Stone Age

From the text:

"Yes," he continued, with renewed animation, "this is a fossil man, a contemporary of the mastodons, with the bones of which this whole amphitheater is covered. But if I am called on to explain how he came to this place, how these various strata by which he is covered have fallen into this vast cavity, I can undertake to give you no explanation. Doubtless, if we carry ourselves back to the Quaternary epoch, we shall find that great and mighty convulsions took place in the crust of the earth; the continually cooling operation, through which the earth had to pass, produced fissures, landslips, and chasms, through which a large portion of the earth made its way. I come to no absolute conclusion, but there is the man, surrounded by the works of his hands, his hatchets and his carved flints, which belong to the stony period; and the only rational supposition is, that, like myself, he visited the centre of the earth as a traveling tourist, a pioneer of science. At all events, there can be no doubt of his great age, and of his being one of the oldest race of human beings."