You certainly don't want them to be hasty, but the sooner they get someone in the position the better. With Arth they had that makeup South Carolina game then took their time and it really put the program behind.
The new guy needs to get in there, start establishing relationships with the viable players on the roster (all 4 of them!) and get out on the recruiting trail. This could also be another big transfer portal year with all of the coach movement and he needs to start accessing that pool of talent along with the JUCO talent. He needs to be a John Groce, a guy who figures out a away to keep the program viable while building it back up.