It started before 1948 even, because although Israel was officially not a state until then, there was turmoil because of people moving there and wanting to start their state on occupied land. If you look at the history there was unrest around WWI already. It just escalated after 1948 because the west legitimized the existence of Israel.
Sorry, I should have been more clear; the actual apartheid started with the creation of the state of Israel (of course). The unrest, suppression, stealing of land and property, and discrimination of people started way before.