Basically every country in Europe has some sort of universal healthcare, most of them for many many decades. Germany actually has had an universal healthcare system for over a century!
The way it works in Germany is, that everyone with an income pays a certain percentage of their wage to an insurance company. Children and people who can't afford paying the rates are insured for free.
Btw the rates are way lower than what you pay in the US. Also spending per capita is way lower in Europe (only half or even lower) than in the US, and the quality is on average much better. We have more doctors per capita than the US, life expectancy is higher, infant mortality rates are way lower, waiting times are shorter etc.
Also every single person I met, who was misfortunate enough, to get seriously ill in the US, and had to cope with the their ludicrous healthcare system was shocked how bad it is compared to European standards.
The only people profiting from the american system are the owners of the insurance and pharmaceutical companies.