When was the first Yom Kippur?

In Israel, Egypt, and Syria. Egypt and Syria attacked Israel by surprise; at the beginning of the war, when Israel was losing, the Syrians had pushed through most of the Golan Heights* (destroying nearly every civilian structure they came across and menacing the most populated part of Israel, which is right below the Golan), while the Egyptians had overwhelmed Israeli defenses along the Suez Canal and entered the Sinai Peninsula**. (It should be noted that while the Golan is still Israeli territory, the Sinai has now been returned to Egypt.) By the end of the war, however, when Israel (with indirect US aid) had turned the tide, Israeli forces had entered Syria and menaced Damascus, while crossing the Suez, cutting off most of the Egyptian army, and approaching Cairo. The war ended when the USSR, an Egyptian ally, threatened to use nuclear weapons on Israel. Even though Israel at the time had just begun its own nuclear program, it did not want to disclose that fact, and probably didn't have the delivery systems to adequately deter the USSR anyway.

*Territory in Northwestern Israel captured from Syria in 1967.

**A large swath of biblically-mentioned desert captured from Egypt in 1967.