Let's set aside the multiple issues with "I think one of my distant ancestors lived here 2000 years ago, or maybe just other members of my religious group, therefore I have a right to live here today" and assume that yes, that sort of historical/ancestral claim gives comtemporary Jewish people a right to live in Palestine. Even in the most generous light imaginable, it would not give them a right to build an ethnostate by committing genocide on the current inhabitants. Israel is so far past anything that could be reasonably granted from ancient Jews living in Palestine that there is no possible defense along those lines.

Or are we strictly talking about western powers giving the Jewish people a 'homeland' after the second world war and the holocaust?

Yes, that's what people mean when they refer to Israel as a colony of Europe/the U.S.

Can I just lay claim to random pieces of land in Africa? I mean all people came from there at one point right?

I declare all of Sweden a homeland for the oppressed Stalinists (I have an incredibly remote connection to Norse settlers along with almost everyone else in my country)

It's a project overwhelmingly lead by western states that has resulted in a huge importing of people who were born and raised in western states pretending they are indigenous to the region. If not for the west, Israel would neither have the resources to maintain its colonial project nor the population needed for occupying Palestine.