They mentioned that their local pet stores aren't carrying live, they may be in one of the states/countries with a live feeder ban, which I'd point to as a breeder-based issue. Hindsight's 20/20, not everyone goes into it knowing to look for an animal already established on f/t rats.
Otherwise, correct. Upgrading this animal over time (aka pinky mice > fuzzy mice > hopper mice > etc) will probably be best to not stress its digestive system with a large jump in prey size, especially if it's already malnourished from its time in the breeder's care. Here's a recent guide on that. It'll be easier to swap once the animal is an established eater so you can afford to have it fast for a few months as it tries to wait you out for another mouse.