You could start with a minimum viable capitalistic state (enforcement of property rights and contacts through police and courts, some sort of government to update laws as necessary, taxes to pay for it all) and from there add basic infrastructure where competition is impractical, like roads, subsurface conduits for laying electricity and data lines, sewage systems, etc; investments that are beneficial to the overall economy but not rewarded by the market like parks, public transportation, and dams; things that ensure a good work force like public education (to supply educated workers) and public healthcare (to keep workers healthy and productive). Optionally you can add laws to improve the free market: consumers can't reliably judge food safety or environmental impact, so make the worst things illegal and improve transparency on the rest (food labeling etc), or impose taxes to mirror true costs to society.

All of this is a free market in your definition, and is essentially how European states are run. But it's somehow not what "free market" advocates in the US want today.

As a European, European countries have a tendency to have not-so-fair rules. Opaque taxation with lots of loopholes if you're willing and/or have resources to go for them. Very different taxation for employees and contractors with loose enforcement who is contractor and who is employee. (Partially) government owned companies participating in the market. Poorly run public purchases. Privatisation gone wrong in sectors where free market just doesn't work (e.g. energy last-mile).

On top of that, Euro side feels like having much much more regulations than US. Which causes it much easier for big companies, but hinder small businesses and upstarts. While technically it may count as free market, it feels like gatekeeping.