The whole claim isn't "first car" but "first production model using a gasoline engine and kind of resembling what we would, today, call a car" ~ and there are a lot of claimants. Benz and Haynes were right close together.
At the same time they were hardly "inventing" the concept of the automobile. All that was happening was the creation of a production method for obvious applications ~ to wit, small gasoline engine on frame of carriage.
Otherwise these vehicles weren't much different than a locomotive.
If you’re looking for production method, then Henry Ford is your man.