Soon after they left the gates, the marching order was allowed to break down. The way they paraded as such was merely for the view of the public. In reality, it was a rather inefficient way of moving, and a shortcut to tiring the men out quickly.
According to their intelligence, the dispatchment that was sent to deal with them was less than a day's march away. They began forward in that general direction with no other plans that they were acting out.
Gengyo did not want this to be a strategical victory. There would be plenty of time for that in the future. He wanted to test the raw power of his men, and this was the perfect opportunity to do that. He would fight this battle almost entirely reactively.
Imagawa had thought that he was playing this safe by sending double the number of men than he knew his enemy to have. He had learned from his campaign into Oda territory, and knew that to underestimate his opponent was folly.
