First let me say that I called the SnowJoe technical support and they could not help.
I am trying to replace the belt that goes around the pulley marked with a red arrow in the below diagram (from their manual). The problem is that the flanged pulley has a shoulder that forces you to fully install the belt around it before trying to install it around the driver pulley. (see the second picture for terminology)
This is for terminology reference, I hope I am using the right names for these parts, I am not a mechanic
Here is what it looks like with no belt
And here is how close I can get without forcing it
To me it seems that the only way to put this back is to use a pulley extractor. Is there a better way?