My answer is a qualified "yes." What I mean by that is that it may seem that the Change character starts out unjustified within the context of the story, but in reality the justification is hidden and pops up fully loaded due to some significant event that "starts" the story going.
All interesting characters (MCs) have ways of dealing with inequities they encounter. The question is how much does it "agitate" them.
Let's look at the movie Big for example. First let's look at the movie as it is--a Steadfast MC. Here is this kid, Josh, who wants to be "big." He obviously has some problems he's dealing with and feels that changing himself would solve them. Suddenly he gets his wish and wakes up one morning in an adult body. This radical event forces him to determine a course of action so he decides that he wants to be a kid again. This requires him to adopt a fully justified (no consideration) position in very short order. Over the course of the story, events wear down his resolve, undermining the foundations for his initial justified position. By the end of the story, he has almost lost sight of his initial position. He's at that teeter-totter stage where it seems as though he could go either way. It only takes a little budge from the kid pal Billy to remind him of his choice (essentially, reminding him of the story limit) and Josh sticks with his original position to go back to being a 12 year old. Thus Josh is seen as a Steadfast MC.
You COULD use the same kind of setup and have the Change MC completely loose sight of the initial position. BUT, in order for it to feel natural, you would need to have some clear-cut rationale for his strength of conviction for his initial position. This implies that there is some deep-seated justification somewhere that supplies the motivation to make that initial commitment seem credible. It could be something obvious like big where something so extreme is introduced that trying to get things back to the way they were doesn't seem like a big jump or require a lot of complex justification.
You know, the more I think about it, I think the nature of Change and Steadfast stories is very different. Steadfast stories are about being Steadfast in an environment of (great) Change. Change stories are about being Changed in an environment of (great) Steadfastness. Whether it's about building up or tearing down probably has more to do with MC Growth. Building up would be START--the need to fill in the gap that is missing (Change) or shoring up a resolve that is being met with greater and greater challenges (Steadfast). Tearing down would be STOP--the need to get rid of the chip on the shoulder (Change) or the process of being worn down by greater and greater challenges (Steadfast).
All About Eve is a Start story in which the MC Changes. Though things appear "normal" at the beginning, the cracks in the "peace" are there from the beginning (Margot is too old to play ingenue roles). Eve's introduction into the equation speeds up the inevitable.
In a way, you could say that Change characters deal with conflicts growing from themselves, while Steadfast characters cope with conflicts introduced by others. Both deal with problem solving and justifications. The difference between problem solving and justification is the difference between dealing with an inequity directly or indirectly.
A story that fits your "unjustified main character building up to justified character and changing" might be Hamlet. Hamlet starts out problem solving. His dad is dead, his mom's remarried, everyone else wants to move on and forget about King Hamlet's mysterious death and the rapid succession of his brother to the throne. Hamlet, on the other hand, dwells on it without any justifications to mitigate his grief. Then along comes the Ghost of King Hamlet who tells Jr. about his murder. Now Hamlet has a LOT of conflict to deal with and he begins the process of justification in order to manage it. He decides that he will pretend to be crazy in order to expose his uncle's treachery. The greater his efforts to expose his uncle and deal with his own grief, the more it tears down his sanity until finally, at the end, he has completely hidden his grief for his father and, in fact, acts as his uncle's representative in a duel against Laertes. He has changed utterly to his great detriment and loss.