The United States certainly does not have a completely free market economic system. It would be almost impossible for any country to have such a system.
All governments must provide some public goods. These are things like police protection and roads. The fact that the government provides these rather than leaving it up to private businesses is one way in which the US is not a 100% market economy.
Essentially all governments ban some sorts of economic transactions. Here in the US, things like drug dealing and prostitution are illegal. In a perfectly free market, no economic activity would be illegal.
Furthermore, the government regulates many kinds of economic activity. It imposes minimum wages. It sets standards for worker health and safety. It sets the age at which people may start working. All of these regulations would not exist in a perfectly free market.
In these ways, we can see that the US is by no means a completely free market economy. We can also see that a completely free market would be essentially impossible in the real world.