In the flashack scene at the end of GF II, Michael says that he has just enlisted in the armed forces. This was depicted as Pearl Harbor Day, December 7, 1941.

Michael and Kay attend Connie’s wedding together in the summer or fall of 1945.

Michael is shown wearing his uniform. Since the war ended a few days after the bombings of Hiroshima and Nagasaki in August of 1945 (Germany had surrendered a few months prior), it is understandable that Mike is in uniform, since he may not have been discharged yet (although the book states otherwise).

Now, suddenly, it is December, 1945, and Michael is going to school (Dartmouth) in New Hampshire.

OK, fair enough. Let’s say he was discharged from the armed forces right around late summer or early fall of 1945, and had just enough time to enroll for the fall semester.

So where and when did he meet Kay?

In the book, however, Puzo gets it straight.

In the book, it says that Michael was 21 years old at the time of his enlistment.

The book goes on to say that he was released (after receiving a "disabling wound", later called a "slight wound") early in 1945, stayed home for three weeks, and then enrolled in Dartmouth.

So from that we may infer that he met Kay some time between his enrollment in college - Spring semester of 1945, probably – and before Connie’s wedding in the summer or fall of 1946.