How were the Hebrews able to establish themselves in Palestine?

Answer 1

If this is referring to history in general, the region of Palestine was the historic Jewish homeland. It would be like asking: How did the Bushmen get to Namibia? -- It's where they come from and where they've lived for many centuries.

If this is specifically referring to the Return of Jews in large numbers to the region of Palestine in the last century, it should be noted that there was a relatively large Jewish minority already present in the region prior to the Jewish Immigration from elsewhere. Those Jews who did arrive immigrated through normal procedures until Israel declared independence. Jewish immigration substantially rose from 1948-1955, especially from the Arab countries which had forcibly expelled their Jewish populations. They came primarily by boats and planes.

Answer 2

The Hebrews did not establish themselves in "Palestine". They established themselves in the sparsely populated land of Canaan, which was later known as Israel.

It wasn't until the Romans expelled the Jews from Israel in the year 70 that the country was renamed "Palestine".

Answer 3

The Hebrews did not establish themselves in Palestine. They were originally from the land of Israel, but when they were expelled by the Romans in the year 70, the Romand renamed the land "Palestine" in honor of the Jews's enemy: the Phillistines.