First off, Pearl Harbor was not an 'invasion', it was what we would now refer to as a raid, or more specifically an air raid. A raid does not suggest or necessitate held ground, it is to enroach on hostile terrain, achieve an objective, be it specific or general, and then egress before a rapid reaction can come about.

The operation on Pearl Harbor's objective was, as someone has already mentioned, to cripple the US Carrier and Battleship fleet. Luck had the US Carriers out on exercise that day, but the Japanese largely succeeded in damaging or outright sinking the majority of the moored US ships. This operation was only a means to an end; the US Carrier Groups and fleet at large were the most mobile forces the United States had, and the most likely to launch relief efforts on US Pacific holdings such as Guam, or the Philippines. The Japanese plan was to cripple US reaction and destroy the isolated Island garrisons piece-meal and at their leisure. Considering that, almost at the same time, the Japanese launched an invasion of the Philippines, which was a de-facto US possession and had substantial US forces garrisoned there, they did indeed 'press the attack', and with stunning results. It led the famous war correspondent Ernie Pyle to gloomily write that 'Make no mistake, we are losing this war' (c.1942).

The US 'neutrality' you speak of is a bit of a stretch. President Roosevelt had been exerting every nerve to support the Allied war effort as best he can, ranging from the lend-lease act for Western Allies, to the outright banning of metal exports to a very under industrialized Japan. The US was already heading towards War, Congress was slowly swinging around, and the United States Armed forces were expanding and arming at a breathtaking rate.

In the context of the time, and without the benefit of hindsight, the Japanese conducted an operation that they believed was rapidly becoming their only option; allow the industrial juggernaut to wake up fully, or launch a pre-emptive strike and set back their combat readiness long enough to (potentially) win with a series of knockout blows. No one knew the risk greater than the Japanese, this was neither a foolish oversight on their part, or a case of ignorance, but rather an accepted risk for a favorable outcome.

The point of the attack was simply to destroy the US fleet. The Japanese wanted to do this so it couldn't interfere with their invasions of the Philippines, Malaysia, Indonesia and various South Pacific island chains. Indonesia was their main target, as it had several oil fields that Japan needed to fuel itself. The Philippines and Malaysia controlled the sea routes to Indonesia, and so had to be captured to secure these sea lanes. The South Pacific islands provided a defensive perimeter that could be used to attrit the inevitable counter-attack from the US. Once this counter-attack had penetrated the perimeter, it would be defeated in a decisive battle that would force the Americans to negotiate. The fleet at Pearl Harbor could intervene in these invasions before the defensive perimeter was set up, so it had to be destroyed.

Pearl Harbor was not an invasion, it was surprise attack to cripple US naval power in the Pacific.

Japan saw war with the US as inevitable by this time. Most in the Japanese military leadership were very well aware that the US had much greater resources and manpower reserves than Japan. However, they badly underestimated the US and Britain's desire to fight back after numerous setbacks.

In the weeks following Pearl Harbor, Japan easily swept through the Pacific and took US, UK and other European colonial holdings. The US's ability to respond to the fall of the Philippines, Guam, and other US holdings was crippled by a lack of an effect Pacific Naval fleet.

Japan hoped that the US and European powers would capitulate and sue for peace since most of them were occupied with a war in Europe and had little to no ability to mount a counteroffensive. This proved to be a tremendous miscalculation. While the Pacific played a major backseat to Europe throughout the entirely of the war, from 1942 onward, the US, UK, and Australia made a coordinated and consistent effort to contain and eventually reverse Japanese expansion.