When I had confirmed I passed the test last August, I sent an email to the ADs of a conference I was familiar with at about 9AM offering my services for Mondays, Thursdays, and a few Saturdays. I had 10 games scheduled by 2PM, including some from an AD that I did not contact. I did not have to travel more than 25 miles for any of them.
I've received multiple emails this week begging for officials for a JH double header on Saturday morning. AFAIK, they still haven't filled the positions.
There is plenty of opportunity for new officials to get games.