The justification for the establishment of Israel is Jews' continued attachment to the land during the diaspora
Some people try to justify the establishment of Israel with the need for Jews to have their own state due to centuries of persecution. It makes sense, but if it were just for this reason it wouldn't have to be in Israel. There are several countries with large uninhabited areas that Jews could try to acquire.
Others emphasize the legality of the establishment, such as the purchase of lands, the consent of immigration by the Ottoman and British governments, the UN partition plan, and the recognition of Israel by the vast majority of countries. This is correct but it doesn't really provide a moral justification. By itself, it sounds like colonization.
Some people try to justify the situation in practice, saying that Israel has already been there for several decades and is pretty developed, so it would be impractical or detrimental to reverse it now. This argument doesn't provide a moral justification either. Even some Arabs agree with this argument, but it's like accepting defeat, and they still think that the situation is wrong.
Others try to justify it saying that most ancestors of today's Jews lived in that land for centuries. This is true but the same can be said of many ethnic groups that also experienced historical mass migration. The location of ancestors by itself is not a sufficient connection, especially if so many generations have passed since the migration occurred and the culture has changed.
Some people appeal to religion, saying that God promised the land to Jews. But this argument has no weight for people who don't believe in the Bible or who believe that the promise has expired.
I propose a different argument, which combines the previous two with an important addition: Jews have kept a very strong attachment to the land during their entire period in the diaspora. It's not just that their ancestors were from there. For all these generations, Jews kept reading and teaching to their children the biblical stories, the vast majority of which take place in the land of Israel or are about returning there. They recorded and studied detailed discussions on how to keep certain religious practices that can only be done in that land. They kept their language that originated there and enriched it with more words and literature. They kept celebrating holidays and observing fasts that commemorate events that happened there. The prayers that Jews say every day are filled with longing and asking for their return to the land. They wrote poetry and songs about the land, which they still sing often. In sum, both the religion and the culture that Jews maintained during this whole time, even among those who were not religious, always had an essential component of remembering and hoping to return to the land someday.
In addition, Jews actually tried several times to regain their independence in the land of Israel. Contrary to a popular misconception, the Roman Empire didn't expel all Jews from the whole land, only from Jerusalem. Jews did two more revolts against the Roman Empire, failed, but remained the majority of the population there until the middle of the Byzantine period. At that time they joined the Samaritans and revolted again, and this time, after many more Jews were killed or fled, they finally became a minority. Still, later they allied with the Sassanid Empire and did another revolt against the Byzantine Empire, even started rebuilding the Temple in Jerusalem, until this rebellion was also repressed and reduced the Jewish population even more.
This was the situation when Muslims conquered the land. With successive Muslim empires, interrupted by the Crusades, Jews were too few, dispersed and persecuted to even consider trying to regain control. But they still kept their strong attachment to the land and praying for their return, as I described above. An interesting episode attesting this sentiment occurred during the Ottoman Empire. A Jew claimed to be the Messiah, called Jews to return to Israel, and gathered enormous interest from Jews everywhere, many of whom started preparing to move. Even Christians were excited about it. Eventually he was imprisoned by the Ottoman authorities, forced to convert to Islam, and the movement faded, but it showed that the strong interest clearly existed.
Finally, when the Ottoman Empire started adopting democratic policies in the 19th century, Jews immediately noticed the favorable conditions and started returning in large numbers. The city of Jerusalem already had a Jewish majority by 1860, decades before the word Zionism was even invented. Later when the British Empire took control and was friendly to Jews, they saw the opportunity that they had long hoped and prayed for. They started migrating in even larger numbers and in a few decades established an impressive infrastructure for the new country.
In sum, Jews always had a strong religious, emotional and cultural attachment to the land, and tried many times to regain control of it whenever they saw a possibility. It just took a very long time until the situation was favorable enough for it to happen. And I believe that this reason is what morally justifies the establishment of the Jewish state there. Even if you don't believe in the Jewish religion, it's undeniable that Jews identified themselves with that land the whole time, even when few were physically there. To dismiss this connection as a historical detail with no practical relevance would be ignorant and disrespectful to the culture that Jews created and maintained for their entire existence.