Note that they're doing a rebuild of an existing house, but the general idea is the same - live in a trailer/old house while you build a garage with an apartment above it, and then move into that apartment and build the main house. This is quite common in more rural areas, such that you can see it even 40 years later; the garage will have an apartment above it, or the barn will have some rooms.
Here's a good YouTube channel with a father/son (experienced) team doing just that: https://www.youtube.com/watch?v=QiOwwhoiKug
Note that they're doing a rebuild of an existing house, but the general idea is the same - live in a trailer/old house while you build a garage with an apartment above it, and then move into that apartment and build the main house. This is quite common in more rural areas, such that you can see it even 40 years later; the garage will have an apartment above it, or the barn will have some rooms.