You give an argument.
Either the person hearing accepts the premises or they don’t.
If they don’t accept the premises, we ask why not.
Is it because they lack the evidence? Fine, give it to them.
Is it because they are pig-headed or stupid? Then that’s their problem and not a defeater.
Is it because they are confused but not stupid? Fine, clarify.
Is it because they don’t accept the premises? Fine, give them further evidence, or, if they don’t accept them for bad reasons, that’s on them.
When you read public reason theory, what's going on becomes clear. The real purpose of public reason liberalism is not to justify rules to a public. They don't even try to do that. Instead, the purpose is to dismiss objections to their own ideology without substantive engagement.