Could Israel attempt something like
Operation Bramble Bush either during the 1950s or 1960s against Nasser
Would it be successful
What would be the impact of either a successful or failed attempt
https://en.wikipedia.org/wiki/Operation_Bramble_Bush
Israel wouldn't do that. Nasser stabilized the different Arab interests to a degree, he was the only one with enough prestige and influence to coordinate the Arab coalition, and to make somewhat binding commitments.
Killing him would have elevted someone to the leadership position, with the same hatred for Israel, but without even the hypothetical possibility to negotiate for united Arab interests.
Without Nasser 67 or TTLs equivalent would have been an even larger clusterfuck.
Field Marshal Amer would have been the likely successor. Being a drug addicted/alcoholic hack, who botched '67 in the first place, the outcome for Egypt is not going to be better.
I don't think Amer had the charisma or previous political successes that Nasser had. He would have been dead in the water after TTL '67 equivalent.
After that you can go two basic routes:
1) Everything is largely the same. Amer is finished and Saddat takes over sooner. Basically does the same as IOTL. Nothing substantial changes, Nasser as a political icon is nearly untarnished though.
2) Amer is finished but in the hysteria of 1967 he reacts badly and Egypt is plounged into chaos. People in Kairo are rioting, Amer clings to power and/or has a drug fueled meltdown.
The Officer's hold on power is threatened and you have a very interesting POD to explore different paths with Egypt.