There are many things which could be seen as philosophical foundations of the United States. Perhaps the two most important are liberalism and capitalism.
Liberalism is a set of political ideas and attitudes. It holds that people have a number of rights that they hold simply because they are people. It is the job of the government to protect those rights. Because of this, liberalism believes in the idea of a limited government. The government does not have the power to simply do whatever it wants. The government has no moral or legal right to do things like taking away freedoms from the people. This idea is clearly shown in our Constitution, which sets up a limited government and explicitly outlines things that the government cannot do.
Capitalism is an economic system that is very much compatible with liberalism. It holds that people should be able to own property and to do what they want with that property. Capitalism allows the people, doing what they want with their property, to direct the functioning of the economy. This is compatible with liberalism since it is based on people’s freedom to do what they want and with the idea that the government should not try to direct the economy.
These two intertwined ideas can be seen as the philosophical foundations of America.