Yes, Israel attempted one false flag attack 72 years ago, intending to damage some empty buildings with no casualties. Still nothing to do with any synagogue.
Yes, the Zionist tactic is to attack, deny, obfuscate, admit but claim that it is not at all indicative of a pattern.
I only gave that example because it cannot be denied. The nature of such ops is to have plausible deniability, such as in the case of the 1950–1951 Baghdad bombings, despite the British, (the ones who are ultimately responsible for the modern state of Israel), concluding that:
"The British Embassy in Baghdad assessed that the bombings were carried out by Zionist activists trying to highlight the danger to Iraqi Jews, in order influence the State of Israel to accelerate the pace of Jewish emigration. Another possible explanation offered by the embassy was that bombs were meant to change the minds of well-off Jews who wished to stay in Iraq."
but there are other examples[1] demonstrating this is not something that is so unlike Israel as you seem to want to portray.