Nope. Zionism only truly started to gain traction at the end of the 19th century and Israel only really began to take shape after the Balfour Declaration in 1917. Prior to this, Palestine was the territory of the Ottoman Empire, and before that it was (for the most part) the territory of various Islamic Caliphates.

The modern conflict we see today can be traced back to the Palestine War (1947-1949) and its aftermath. So yeah, 50+ years is pretty accurate. Saying it's been going on for thousands of years is a common misconception. Some people try to perpetuate that misconception in bad faith to conceal the fact that this whole thing started because colonial powers stuck their business into a situation where it didn't belong.