A big part of its success was the collapse of USSR. So luck and ability to self-reflect and realize on their fortunes and execute on that lucky break...
In the 90's they had a population of 4mil and something 300k Soviet immigrants were arriving every year. A large proportion of them was highly educated people. And those people who sent rockets to space were cleaning the streets...
So what they did right was just take money from US grants and give that money to everyone who wanted to build something and asked for it. They have built these huge warehouses/offices called "hothouses" on the outskirts of cities, put the unemployed scientists there, gave them some money and said build something.
Yes, I think a lot of thier curreny success comes from "exchange" with larger countries and a natural incentive to develop e.g. military technology. I guess it is similar to places like Taiwan.
If you removed all the US companies, restricted immigration and didn't allow people to go abroad to study it isn't clear how well they would do. From what I hear it is no dream to be young in Israel today. Also there seems to be a surprising amount of shady things coming out of Israel. Anything from spam and exploits to binary options and outright fraud. Which would suggest that people don't have better opportunities.
I think this book https://en.wikipedia.org/wiki/Start-up_Nation mentions it, but I don't know any source that writes in details about it.
All from my memory of seeing relatives and friends that worked for Soviet research institutes --> sweeping streets in the desert sun at +40 Celsius ---> working on interesting hardware/software projects. It's amazing how people can thrive and pull out of the lows if you give them a hand. Completely the opposite happened to people in Russia, these research institutes were shut down and people just succumbed to alcoholism. Decades of knowledge were lost or just transferred to the US defense industry.