Historical ignorance at its finest.
That spark — the claim that Israel had been massing troops near the Syrian border — was a Soviet lie, and everybody knew it. The Egyptian chief of staff personally inspected that border, the Syrians themselves sent reconnaissance planes. They found nothing and discarded the claim. Eshkol even suggested to the Soviet ambassador to jointly inspect the Israeli side of the border — he declined.
Neither in Israel nor Syria did foreign press report any mobilization, which on any larger scale would have been absolutely unconcealable.
Yet on the 15th May — Israel's Day of Independence — Nasser announced a military emergency and started to sent the first two armored divisions into Sinai.
Nasser expelled the UN troops on the 16th May. Israel started partial mobilization only on that same day, full on the 19th.
By the 17th, Egypt ordered its armed forces to take up battle positions in Sinai.
By then three Egyptian divisions with more than 600 tanks had began fanning out through it. Damascus was simultaneously mobilizing 50 cadet battalions, Iraqi brigades were moving towards their Jordanian border. Kuwait, Yemen and Algeria announced readiness to dispatch troops and planes.
(Ultimately it would be 1,300 Israeli tanks vs 2,500 Arab ones, 746 artillery vs 2,780, 247 fighter jets vs 557, etc.)
As late as on the 20th, Israelis tried to get De Gaulle mediate with the Soviets, and requested Washington to make good on Eisenhower's 1957 declaration to demonstratively send a warship through Tiran — no response was forthcoming.
His successor Sadat would later recall Nasser's own words: "Now, with the concentration of our force in Sinai the chances of war are fifty-fifty but if we close the Straits, war will be a 100 per cent certain."
Nasser would close said straits, recognized in 1957 by the maritime nations as international waterway, to Israeli shipping on the 22th.
In a speech before unionists on the 26th, Nasser would boast: "The battle will be a general one and our basic objective will be to destroy Israel."
No Israeli PM would ever say anything like this.
Nor would Israeli troops ever publicly march through Tel Aviv chanting "We are off to Cairo."