work their way up

[keannu]

work their way up seems to mean, in dictionaries, "make a big break", but does it here mean just physically "going up"?

mo2-36
ex)The Maleo is a medium-sized blackish bird with a reddish-orange beak...After the eggs hatch, the young birds work their way up through the sand...

[Tdol]

Yes, because the eggs are buried in the sand: Maleo - Wikipedia, the free encyclopedia

[Raymott]

work their way up seems to mean, in dictionaries, "make a big break",

No, it doesn't mean that. It means to start low and, by hard work, end up somewhere higher. It's usually a slow process that has nothing to do with "making a big break".