Copied, with slight changes, from an earlier response of mine:

Variations on this question come up with some frequency in this sub, and I have answered them a few times. You can read a couple of those answers here, and here.

With more specificity, I have addressed the question of the difference in accents between George Washington and King George III in an answer here.

I have addressed the question of the development of regional accents within America by the time of the Revolution in an answer here.

I have addressed the related myth about the American accent being "closer to the original British accent" or Shakespearean or Elizabethen English in an answer here.

To paraphrase again: there was likely a distinct American accent just as soon as there were enough American-born adults around for English/British visitors to converse with to notice. This could have happened as early as the late 1620s in Virginia and the early 1640s in Massachusetts, though the initial American-born populations were tiny. They were swamped by a much bigger influx of English immigrants shortly after the colonies were established. In Plymouth and Massachusetts, this coincided with the Great Puritan Migration that started with the Winthrop Fleet in 1630. Thus, it's likely an accent wouldn't have been noticed until about mid-century, since so many of the adults until then would still have been immigrants.

According to historian Paul K. Longmore, there were enough American-born English speakers by the 1670s that English visitors would have noticed a distinct American manner of speech. Historian and language scholar Allen Walker Read found evidence going back to 1663 of commentary by English visitors on how Americans were using words and language differently from how the language was being used back in England. From that point forward, there is regular indirect evidence that there was a separate American accent from any accent heard back in England.

The first direct evidence of an American accent comes from Hugh Jones, an English-born professor who taught at the College of William and Mary in Virginia between 1715 and 1721. After his return to Great Britain, he wrote a book called Accidence to the English Tongue, published in 1724, which described some of the new innovations of American speech (like pronouncing the letter s in some words closer to z as in "has" and "raspberry"). He also commented that the American accent was much more uniform and much more old-fashioned, which he considered a good thing since he thought the accents then developing in England were uncouth.

From that point forward, there are regular mentions by English visitors noticing the American accent, or English immigrants sticking out as a foreigner. In fact, as early as 1739, Benjamin Franklin had written in Poor Richard's Almanack about regional differences from colony to colony in the American way of talking.

By the time of the American Revolution, not only was "the" American accent commented upon regularly, but regional and social dialects were being commented upon as well.

You might want to consult this sub's FAQ as well, which provides some other answers to this question in addition to one of mine.

While not in the FAQ, you may also want to consult this post by /u/YuunofYork, who answers the question from more of a linguistic point of view rather than a historical point of view.