1897 - Wesley Dodds is born.
1916 - 19-year-old Wesley goes to fight in WWI
1919 - 22-year-old Wesley returns from war & becomes a cop.
1921 - 24-year-old Wesley is promoted to the detective bureau.
1925 - 28-year-old Wesley leaves the police force & becomes a private detective.
1932 - 35-year-old Wesley, still unsatisfied with the limits of the law & plagued with prophetic dreams, dons his gas mask & becomes Sandman.
1939 - WW2 begins.
1941 - After the attack on Pearl Harbor, The Justice Society is formed, including 44-year-old Wesley.
1945 - WW2 ends.
1951 - 54-year-old Wesley is trapped in Ragnarok with the Justice Society. He dies trying to escape.
The Sandman name has been weirdly prolific, considering how unrelated a lot of the various characters bearing the name have been. Wesley Dodds, the character we're using, is an interesting time capsule from the Golden Age. His trench coat & gasmask visage is a throwback to a style of character we really don't get that often in comics anymore. He went on to adapt a far more generic superhero costume and a kid sidekick, who went on to become the modern Sandman, a character who ultimately donned an outfit similar to Wesley's original look. We're leaving him out because he's always felt a little redundant.
There's also a briefly-used Sandman character in the mid seventies that would be completely forgettable if he wasn't one of the creations of Joe Simmons and Jack Kirby. Whether or not we include the character (we don't), it's still a great read just to see more of their work.
Then of course, there's also the most famous version, Neil Gaiman's Sandman from DC's Vertigo imprint, a book very high in the standing for greatest comic series ever. There were early attempts to establish that the book was set alongside the DC universe proper, both by giving characters from the Justice League cameos early in the series and by establishing that Morpheus's imprisonment was responsible for Wesley Dodd's prophetic dreams. The Vertigo characters DO exist within the DC continuity, even in out timeline, but trying to create a timeline for the Endless would be pointless. We can simply understand that they exist and allow Wesley to be the sole representative of the Sandman legacy within our story.