This is a popular question and there seems more and more to be added on the subject so I hope it doesn't discourage any more answers or discussion.

/u/lord_mayor_of_reddit gave a good answer to this [question] (https://www.reddit.com/r/AskHistorians/comments/5toz0o/how_and_when_did_the_american_accent_come_to_be/)

I'll quote the TLDR :

"TL;DR version is that there's evidence of American accents before 1700, and more circumstantially, an accent separate from any heard back in Europe began to develop by the mid-1600s with the first American-born generation of English speakers."

/u/keyilan writes in the answer to this [question] (https://www.reddit.com/r/AskHistorians/comments/8cvhob/when_did_americans_lose_their_british_accents/) how accents was changing within a generation and that it is not a unique phenomenon to American colonies and that all accents go under continuous change. As an example Cantonese speaking people in Calcutta underwent similar changes.