Israel was founded by Lehi, Irgun, and Haganah. The evacuation plan which led to the population growth of Israel was invented by Irgun commander Ze'ev Jabotinsky. The sixth prime minister of Israel, Menachem Begin, was also a commander in Irgun. Irgun and Lehi led to Herut, which is now the modern controlling Likud party in Israel. Lehi also had Yitzhak Shamir who became prime minister in the 1980s.
Lehi is famous for the Ankara document which proposed a pact with Nazi Germany to help start a totalitarian state (their words) in Palestine, to fulfill Zionism. They sponsored multiple sabotage and espionage operations against the British and in the Middle East. They were instrumental later in the invasion of Iran in 1942.
Lehi assassinated politicians in Britain and was described as a terrorist organization by the British authorities.
Irgun is an even easier case to make. Its motto: a hand holding a rifle with the words "only thus" underneath it. It was self-described as a terrorist organization by spokespeople from it at the time (1940s) and openly spoke of terrorism as the only effective way for a Zionist state.
So yes, Israel exists because of terrorism and is deeply rooted in it at a fundamental basis.
The whole point is that to point out that the current political manifestation known as Israel is a danger for the geopolitical stability of the region is actually a valid observation that historians will see as clear as day in 500 years. I know how politically unwise it is currently, but that doesn't make the reality false. There's lots of bitter pills out there.