They let people line up for Ministry at early entry and usually letting people on the ride about a half hour before park opens. I suggest doing it first as it can break down later, and if you’ve only waited 30 mins to ride (vs two hours) and it breaks down it’s not such a big time suck of your day.
They purposely do not dump the queue for most breakdowns, which means you will have to stay in line and wait it out, or you wasted time in queue and when you come back to ride again later, you’ll have to wait again. For me, it’s not worth the risk (because I’ve waited HOURS just waiting in that line just to never ride that day, and that’s not a good use of your time). Ride first, ride early, no more stress to get on all day.
Nearly all of the Unofficial Guide touring plans suggest riding Ministry first, for many reasons. But for me, it’s to ensure I get it done first and relieve the stress of worrying later. Plus, it’s a great way to start the day! Extremely impressive queue and ride to set the tone.