Note that this is subtly different from the “one level in every class” thing; this is about taking your levels one at a time, starting from level 1, rather than a fully-finished level 13 concept.
Could this be at all viable? What order would you go with?
There are many good reasons that almost nobody actually tries to do this in a real game. Sacrificing some mechanical optimization for flavor and sticking to a particular concept is one thing, but if you’re going into more than three classes total you’re either aiming for some sort of hyper specific niche build (which is probably still going to include multiple levels in most of it’s classes even if there are four of them) or “lOl So RaNdOm” idiocy that’s just going to result in a ridiculously incompetent character compared to any other PCs that are single or dual class.