Governments will provide capital for startups and I've seen many entrepreneurs over the years take advantage of this form of financing. The grants are usually "free money" in the sense that they do not need to be paid back and they don't cost any equity.
But nothing in life is free. You do pay for this money in ways that may not be in your interest. The application process is usually long, involved, and distracting. And sometimes the grants come with strings attached; you can't move, you have to use it for a specific purpose, you have to hire a certain number of people with it, etc, etc.
I've seen states provide grants to do "economic development." I've seen all sorts of US Federal Government grants. The most common are Small Business Innovation Research (SBIR) Grants. But there are also grants available from various departments related to energy, health, defense, and many more. Internationally, I've seen Canada, Israel, and Slovenia provide "free capital" to startups.
In Canada, startups can get a portion of their headcount funded by the government. In Israel, the government provides grants to startups but they need to keep their IP in country. I am sure that many countries around the world provide funding of this sort. And I suspect we will see more of this sort of thing as technology based economic development becomes more important.
I'm not a fan of this form of financing. First, in principle I think that government ought to stay out of the business of picking winners and let the market do that. But more practically, I've never seen an entrepreneur change the outcome of their startup with government money. It is never enough to really move the needle and the strings that are attached usually make it uninteresting to me.
But if you would like to look into this sort of thing, contact your state and national government and ask about grants for high technology, research, and startups. I suspect you'll find some programs out there that you can tap into.
