Ummmmm.... no. I am disappointed how many folks don't get "free markets". Market forces are powerful but they are motivated by profit. Nothing wrong with this, but as intelligent citizens, we need to understand how this works and their limitations.
One limitation is that if profit cannot be privatized, then there is little if any incentive for market dollars to pursue R&D or other activities. Where is the profit in finding ET? Even if you come up with an answer, then how do you limit the profit to those who make the discovery. You can't. So, market dollars will not pursue this project. This means you are looking for a benefactor or a government entity to fund this. There is nothing wrong with government funding of projects that the free market would not undertake... as long as there is a public good to the investment.
So, no, the free market is not a magic bullet to solve every problem.