This question gets asked frequently on this sub and I have answered it at length before. If you don't want to read that whole wall of text, then briefly:

There were differences in language noticed as early as the 1660s. There's indirect evidence of American accents between the 1680s and 1710s. The first direct mention of American accents was published in 1724 by a visiting professor to the College of William and Mary, who taught there between 1716 and 1721.

Accents were written about more and more frequently between the 1720s and the Revolutionary War. By the time of the Revolutionary War, several different regional accents had been written about, including New England accents, southern accents, black American accents, and others.

Some answers to this question often say something about the English spoken in Appalachia, or the Tidewater region/Tangier Island, Virginia, being close to how Elizabethen English used to sound, but that's a myth. In fact, by the time of the Revolutionary War, the Tidewater accent had already been mentioned as being a separate accent from the more general accent heard in the southern colonies.

Sources on all this can be found at the link at the top of this post.