One could argue that the history of military vehicles harks back to the days of chariots and siege engines, machines that relied on animal or human power for their propulsion.
However, these types of machines eventually became obsolete due to more sophisticated tactics in wars and battles and there was very little invention in terms of propulsion for hundreds of years until the advent of steam, which in itself only inspired the creation of a few military vehicles. One such example was James Cowan's steam 'battle car' of 1855, which never gained any popularity because it was deemed uncivilized.
Of course, despite strong ideas of the correct way to fight, the mechanization of the military was inevitable. The impact on nations' armies by technology started to become clear as more and more armies began using steam tractors to transport troops and weapons. However, petrol/gas engines were more efficient and versatile and by the start of the twentieth century guns and armor were being added to commercial automobiles.
Armored cars were developed during the years leading up the the First World War, but after a year of fighting it became obvious, because of trench warfare making the war a very defensive affair, that these cars were useless - something better needed to be invented.
Armies wanted new ways of traversing trenches, shell holes and barbed wire as it was the infantry that endured most of the fighting in these circumstances and took extremely heavy losses.