Hard to diagnose from a distance, but I had exactly the same symptoms and similar setup (a belt drive with an excentric bottom bracket).
I couldn't really find a problem but the sound went away when I put grease on the bottom bracket, so I left it at that. Then a few months later the axle in the bottom bracket very suddenly became totally loose, within a few kilometres from fine to 2-3mm play, and the noise was back.
Bike shop looked at it and found that the bearings inside the bottom bracket were held by a plastic bit that just disintegrated, so I had to get a new bottom bracket. It was probably cracked much earlier, creating the clicking sound at every turn, but then had settled into a non-clicking position before failing totally.
The bike shop also said that they know that in my bike model the bottom bracket is a bit cheaper than it should be, good enough for most people, but too weak for a heavy rider in a hilly city. So they put in a much more solid bottom bracket. So I think it is worth asking a bike shop that sells your model of bike about their experiences.