Lou Gehrig began his streak today in 1925

On June 2, 1925, Lou Gehrig, who had been playing for the Yankees for two years, but never as a regular player, took over for Wally Ppp.

From Wikipedia:

On June 1, 1925, Gehrig was sent in to pinch hit for light-hitting shortstop Paul "Pee Wee" Wanninger. The next day, June 2, Yankee manager Miller Huggins started Gehrig in place of regular first baseman Wally Pipp. Pipp was in a slump, as were the Yankees as a team, so Huggins made several lineup changes to boost their performance. Fourteen years later, Gehrig had played 2,130 consecutive games