Tire change question

i am a new owner of used 2012 exmark Viking with a tire that has gone flat or got off the hub of the wheel. I have already put a brick underneath the mower so I can work on the tire. I've tried examining the tire for any punctures and I have not seen any thing. What is my best course of action 1. Refill the tire and see if the tire seats or 2 remove the tire front the mower.

Also I'm a little confused as to how to get the tire off. I've attached a picture Of the assembly. Thanks...

Tire change question