Land belongs to whoever controls it. That's it. That is all it will ever be.
If there is not some higher power (e.g. the UN, who you say does not have authority), you have no recourse.
No matter what land it is or who they are: nobody currently living was there first. The only claim is always "I was the last to control it". But none of us are the first.
> "Most of Palestine's population, estimated to be around 200,000 in the early years of Ottoman rule, lived in villages. The largest cities were Gaza, Safad and Jerusalem, each with a population of around 5,000–6,000."
OP's point was "Under the Ottoman Empire it was (relatively) scarcely populated and a mix of Jews, Christians and Muslims, plus some religious minorities."
What are you trying to dispute here? That the territory of today's Israel was sparsely populated back then, or that the Ottoman Empire existed back then?
> Almost no Jews at that time either.
What a wild claim: almost no Jews in places like Jerusalem? Please cite whatever source you have to make such an extraordinary claim.
Exactly the part that you left out: that the Jewish presence (before zionist immigration began) was of any relevance in the demography of the region.
Source for census data:
https://en.m.wikipedia.org/wiki/Demographic_history_of_Jerusalem
False. The population in 1800 was ~90% Muslim, ~8% Christian.
> let's not forget that the partition plan for Palestine was proposed by the UN
The UN had no authority to partition other people's land.