Belle Tire doesn't do appointments for alignments, or any other type of service for all that matter. That's all first come first serve. I wouldn't necessarily say a master tech has to do it either, though. An idiot could do it with the Hunter machines and enough time, assuming everything you have is adjustable. Also, depending on exactly what is being adjusted, be prepared to pay slightly more for a 'front end alignment' since technically most cars only have a few minor adjustments and probably nothing close to what you're doing.
As someone else said, show up before they open and be prepared to wait. That's really the best idea anyhow. Tell them you're waiting, too - so they know. That way the tech will want to get it done ASAP so he can move on to his other stuff. If they ask you to come back later, then you can ask for a specific time.