Israel wiped out air support for the Egyptian military by striking the first blow and wiping out Egypt's Air Force. This meant that Egypt would not be able to launch a meaningful ground invasion.
At this point, even assuming Naser was going to invade Israeli territory in the first place, the war was over. Egypt could not have launched a ground invasion, even if it wanted to. But Israel proceeded to take the Saini. At this point, in the words of historian Tom Segev, the war was no longer a war of necessity but became a war of choice.
> Egypt and Jordan were literally broadcasting to the world that they were planning on wiping Israel
No they weren't.
It's well known that the Israelis regarded the Egyptians as posing no existential threat to them
It was a pre-emptive strike. i.e Israel started it.