What period of time did dinosaures become extinct?

That depends whether you believe in the view of modern science, which says it was millions of years ago..... or alternative history, in which case it could be only about 20,000 years ago.

If you read the works of Edgar Cayce on the Origins of man he talks of times when Atlantis was still a great continent, and people from many places on Earth got together to discuss the problem of giant creatures which were a great danger to man, and how to get rid of them.

I can only assume they meant carnivorous dinosaurs, and since Atlantis finally disappeared beneath the ocean about twelve thousand years ago, they may have been around much later than modern science tells us.