In 22:5 Balak says to Bilaam, "הנה כסה את עין הארץ" - that Sichon and Og, both of whom we relied upon for protection, were defeated by the Jews, so we would have no chance against them.
So just be peaceful and let the Jews pass and don't make trouble! The Jews did not start up with Sichon and Og - Sichon and Og attacked them! So if you are afraid of the Jews, just leave them be. If you do not attack them, they will ignore you as well. Why look for a better way to defeat them?
Eveybody lives in their own reality. We look back to Parshas Chukas and find the Jews making their way peacefully to Eretz Yisrael when Sichon and then Og both start up and attack them. Balak's reality was that the Jews were powerful warmongers, starting up with all the nations they come into contact with. They aleady defeated them, and we are next in line.
There are two (or three!) sides to every story. Everyone has their own reality and their own perspective, and they act based on their own reality.