This question is not really answerable as is. Defining who's Jewish and who's not is extremely difficult in the earlier parts of that time span (calling them Jewish at all is an anachronism, but I'm ignoring that for the moment). It's also difficult later on, with the Samaritans. What's more, historical demography is a huge challenge, and there'll be a lot of uncertainty over anything. Additionally, the modern borders of Israel/Palestine are not reflective of the specific borders from any particular past time, so censuses and administrative stuff can't answer the question exactly, and the answer is meaningless in many eras.

I can, however, tell you what eras had a large Jewish population in the region, that may indicate a majority. I'm also counting Samaritans as Jews, since this time period begins before they split, and exactly when Jews became dominant over Samaritans is unclear (and what demographic realities it involved), as is when Samaritans had the upper hand again.

So Israelite groups (that's Jews and Samaritans) seem to have been a dominant force in the region until roughly the Muslim conquest. I don't know of any good analyses on when Christians got numerous in the region, but when the Muslims conquered those two groups made up a majority of Palestine, and did for some time after. Jews were the dominant group in towns, whereas Christians were the main group in rural areas. At some point before the Crusades, Muslims became the majority, though there were substantial Christian and Jewish minorities. After the Crusades, Jews still lived in Palestine, but were a relatively small minority group until the 20th century.

source: Gil, Moshe. A History of Palestine, 634-1000