Jews from the first Aliyot certainly bought land, often from Turkish effendis who lived far off. They brought their own people to work it, evicting Palestinian Arabs. Land purchase, in fact, became so controversial that the White Paper of 1939 prohibited further Jewish land purchases w/o Arab approval.

That being said, yes, many Palestinians were driven off their land by Jewish militias in '48; others fled & were not permitted to return. Ben Gurion, in fact, delayed signing an armistice in order to the IDF opportunities to occupy more land.

Later, many who fled were not permitted to return & the sites of their villages were rendered uninhabitable.