Here are some strong contenders:
* Cugnot's Steam Carriage (1769): This is often cited as the first self-propelled vehicle. Built by Nicolas-Joseph Cugnot, it was a three-wheeled steam-powered vehicle designed for hauling artillery. While it could only travel a short distance before running out of steam, it was able to move under its own power.
* Richard Trevithick's Steam Carriage (1801): Trevithick's steam carriage was a four-wheeled vehicle that could travel at speeds of up to 5 mph. It was used to transport passengers and goods, and it played a significant role in the development of the steam locomotive.
* The "Puffing Devil" (1802): Designed by Trevithick, this steam-powered carriage was the first to be used commercially, running on rails. It was used in a quarry in Wales and was one of the earliest examples of a steam locomotive.
Therefore, depending on your definition of "vehicle" and "self-propelled," the first self-propelled vehicle could be any of these.
It's also worth mentioning that early steam-powered boats were also developed around the same time period.
The development of self-propelled vehicles was a gradual process, and it is impossible to say definitively which invention was the absolute "first."