Many users will first learn of their suspension when they see their reputation score go down to 1. I disagree with the reasoning behind this (beyond "the reputation / privilege system forces this behaviour"), but changing the behaviour would be hard.
Instead, users who learn they're suspended by seeing their reputation score go to 1 should also learn that they're suspended. (This has been suggested a few times over the years, most recently here.) I envisage it looking something like this:
This should only display for the suspended user, and it should display everywhere that the reputation score is visible. The link should take me to a help page about suspensions in general, or to the moderator message explaining my suspension in specific.