There is no record of ASL starting before 1814. ASL was formed with the help of Thomas Gallaudet and Laurent Clerc. Clerc was Deaf and he came from France and he agreed to come back to the USA with Gallaudet to establish a school for the Deaf in America, the school was established in Hartford, Connecticut and is now know as the American School for the Deaf.
Gallaudet work in helping establish the school for the Deaf in America was really crucial in helping form what would become ASL. ASL was formed from signs that the Deaf students who attended the school in Connecticut brought from home as well as signs from French Sign Language as well. To this day the USA is the only country to have a fully Deaf university. The university is in Washington D.C and is named after Gallaudet.