Steve (Serviside Blog) the most incredible researcher I've ever met or heard of, has already posted that the steam powered wagon race in 1878 in Wisconsin was the earliest documented, http://serviside.blogspot.com/2011/10/first-auto-race-pet-peeve-and-hazards.html
and that predated the 1887 De Dion Bouton time trial in Paris
So that was what I was posting about in 2013 https://justacarguy.blogspot.com/2013/10/the-first-car-race-happened-when-worlds.html
But yesterday Stephen sent me a link to an 1867 race! https://www.theengineer.co.uk/content/archive/august-1867-the-first-motor-race
and here is the newspaper record of it https://www.theengineer.co.uk/media/hxohcozt/aug-1867-the-first-race.pdf
The race was contested by “two road steam carriages”, one constructed Mr Isaac W Bolton of Ashton-under-Lyne, the other by Messrs Daniel Adamson and Co of Newton Moore.
“Mr Isaac W Bolton of Ashton-under-Lyne having only one four and 1/4 inch cylinder 9 inch stroke, the other, made by Messrs Daniel Adamson and Co of Newton Moore, having two cylinders 6 inch diameter 10 inch stroke.”
Run over a distance of around 8 miles, it took place between Ashton-under-Lyne and the showgrounds at Old Trafford, getting underway at 4.30am, possibly to avoid the attention of the authorities.