It's pretty simple:
-Sonny beats up Carlo and behind him there are specifically placed Thomas Dewey 1948 election posters, meaning it's probably sometime in 1949, or perhaps even as late as 1950.
-Sonny is listening to a broadcast of the baseball playoff game won by Bobby Thomson hitting the Shot Heard Round the World just before he was killed. This happened October 3rd, 1951. This was put in specifically.
-Vito's tombstone has his death date as July 29th 1955. Many of the cars in the later scenes (after Michael returns home) are 1950s cars.
-The novel has Vito's death as being specifically just about TEN YEARS after Connie's wedding. Connie's wedding is established as Summer 1945. This would put Vito's death, even in the novel, as being sometime around or during Summer 1955.
-The script for Godfather I has the ending (from Michael's trip to Vegas on) as being in 1955. It has Michael returning in the Spring of 1951.

The only point of contention in the timeline is Sonny's death. The script has it as early 1946. This makes sense. The War couldn't last for years and years, and it wouldn't take Vito six years (1945-1951) to recover from his wounds enough to run the Family. It'd only be a matter of about 6-8 months probably--Still a long enough conflict to cost The Families a lot of money.

The Dewey posters are explainable: They're just leftovers from the election of 1944, which would've been only just a little over a year before 1946.

If Sonny dies in 1946, the Don begins arranging for Michael's return sometime after the Commission Meeting--which was probably a few months after Sonny' death. It takes a few years due to the publicity surrounding the murders of the Turk and Sollozzo. Michael returns in early 1950. The Sicilian has 1950 as the year of Michael's return and it falls in line with Michael telling Kay he'd been back a year. In the Senate scene in II, the Chairman states that Michael devised the slayings as of the other heads of the Five Families in 1950--which make sense when you see the deleted scene with Michael and Vito, where the seeds for the Massacre of 1955 begin to be planted.

Vito needs a few years to teach Michael the ropes of how to run the Family and manage the front organizations and maintain the Family's political contacts, as well as formally give Michael his button. They also need a few years to begin their plans for the move to Nevada (not something you do overnight), and how it will be handled, along with a few years to have Rocco slowly build a regime in secret. They do it slowly, lulling the other four families into thinking the Corleone Family has grown weak and complacent in peacetime, which allows Barzini to begin chiseling away at Corleone territory.

He meets up with Kay again sometime early in 1951; They're married and she gets pregnant not long after, probably giving birth in late 1951--Which allows for Anthony's confirmation in 1958.

Vito dies in the summer of 1955--Anthony in the garden with him appears to be about 3 or 4. This makes sense if we consider that he was born in late 1951.

Really, the beginning is 1945 and the end is 1955. The only thing worth debating is the exact dates of what happens between those two dates.