Was war between Japan and the USA was inevitable or simply the most likely outcome?
It has to be remembered that the USA held back after Japan went to war with China in 1937. They didn't want to provoke Japan into a greater conflict but, eventually, Roosevelt began sending aid to China (1940). It also has to be remembered that the USA was the main supplier of oil, steel and iron to Japan. When they began an imbargo of all goods that could be used by the military, this loss hit Japan hard. The war with China was getting bogged down (worsened by the American aid now flowing there) and Japan's war machine was in danger of grinding to a halt. This left the Japanese with very little room to manouver. They needed raw materials and looked south.
They did have the concept of the Greater East Asia Co-Prosperity Sphere with the populist slogan Asia For The Asiatics. This had been an attempt to break away from Western domination with Japan becoming a major player in something like a 1930s version of the EU. In reality, it was simply a way for Japan to extend dominance over other asian nations, and now it became an effective propaganda tool to help whip up popular support.
It was never Yamamoto's intention of defeating America - he knew that he couldn't do that, but he had seen what the British had done to the Italian fleet at Taranto and formulated the attack on Pearl Harbour. He knew that the best he could do was inflict such devastation on the US Pacific fleet that they would be driven to the bargaining table but, of course, that was never going to happen. He didn't know the USA as well as he thought he did.
When it comes to Japan, I always come back to the same question. They must have known that they were never going to win but they did it anyway. Why? Of course, it's difficult for us to understand the mentality but the militarised and warped Code Of Bushido had been appropriated by the hawks in Tokyo and there was very little liklihood of any other path to take. If cooler heads had prevailed war between the two might never have happened. Of course, we then come to the point where such nationalistic fervour would look upon anybody talking of peace to be a traitor to the cause. So, to go full circle, and with all that in mind, perhaps it was inevitable after all.