|With that in mind, here is a website that federal agencies do go through to solicit grant applications: Grants.gov. Please note that a typical grant application would be to a very specific PART of the free money from the government, such as the US Department of Education, Pell Foundation, not just "the government." There would be intense competition for the grant and a complicated application process.
You can also seek private foundations through The Foundation Center. Here you will find very specific founders as well (like The Bill and Melinda Gates Foundation) with very specific missions. If you can assist the Gates Foundation in bringing clean drinking water to the third world, for example, or improving educational opportunities for high school sophomores in King County, they're looking for you.