When did the American accent originate?

The custom of the English language in the US was a result of British colonization, which commenced in North America in the 17th century and immigration occurring in the 18th and 19th centuries.

Where did the standard American accent come from?

It is based on RP (British Received Pronunciation) which was adopted with American alterations in the early 20th century by linguist William Tilly. These alterations, this authentic “American” sound was loosely based on the speech of North Eastern population of the US.