It's not like they are thinking, 'hey let's go for a long swim', but they do go into water to eat and swim and if they got turned around or a current brought them away from land or a storm came upon them, they have no choice but to keep swimming. So some very small percentage could stumble upon it that way. All you need are a couple (or 4) to get a population started, and if some new moose got added to the genepool via a water crossing that would help a genetically bottlenecked population tremendously.

And at first glance 110K from 4 moose seems like a rather large population boom. But they can produce 1-2 offspring per year, so not accounting for deaths and a best case scenario that can grow rather quickly, and if you can sustain 110K moose there are way more resources available than needed for a much smaller population so resource constraints wouldn't be a problem at least. A few decades and some luck is all they needed.