You could also look back. History has many examples of people governing themselves in various ways that differ from the systems used at the moment. Even within the spectrum of contemporary democracy, there are several options to choose from. People could just look up what kinds of democracies are used in other countries and how they differ from the one used (or not used) in your home country.
I think we need a new radical philosopher who comes up with a new way of government, and starts promoting it actively. Actually, long ago, I heard a small political party do just that. They wanted to switch to the kind of direct democracy used in Switzerland, which sounded nice IMO. If people heard about someone proposing an alternative, they might at least consider it.
The way I see it, people aren’t really exposed to different ideas of this kind. They see the problems, but not the answers. People aren’t really proposing new solutions that much, now are they?
Ideally, you would find a “philosopher king”, but that’s unlikely to happen. The next best option would be liquid democracy or some sort of direct democracy. If that’s not an option, you could switch to preferential voting that leads to a coalition parliament fairly often. Proportional representation works too. Basically anything other than FPTP.