The answer is more frightening than it appears on surface. Yes, the Egyptians had a real chance to severely disrupt, if not destroy, Israel in 1967. By May 16, Egypt had amassed 85,000 troops in Sinai with 100,000 in reserve, including reinforcing their airfields which were now in reach of Dimona, Israel’s purported nuclear production center. The UN peacekeeping forces evacuated without protest upon Egyptian President Nasser’s orders. Syria was increasing their harassing attacks in the North, ensuring a two front conflict. A week later, Nasser blockades the Straits of Tiran closing Israel’s southern port and only access to Asia; whose preservation was guaranteed by the US since Eisenhower. In 1967, they were otherwise occupied. Israel was alone.
Egypt’s key to winning was based on parity, not superiority, in the air. Though outnumbered and lacking strategic depth, Israel’s army was better trained and decidedly more determined. It may have not been enough to prevent disastrous casualties. Egypt planned to attack Israeli cites, along with the military targets, which could divert Israel’s resources The key to Israel’s winning was a surprise attack on Egyptian and Syrian airfields before their planes could take off to remove this threat.
They observed their enemy’s actions closely, and found a weakness – security was lax during the changing of the guard and there were gaps in the radar coverage. At 7:45 on June 5, Israel launched a simultaneous air and land attack. Its success depended on the air force’s ability to disable Egypt’s air force. Unexpectedly, Israel employed 90% of its aircraft , leaving only 12 to defend its cities. Thusly deployed, they were wildly successful, effectively winning the war in the first few hours.
West Point teaches the victories of the Hashmonean and Roman revolts. They do not teach the battles of the ’67 war because it had a low probability for success.