This doesn't really capture the idea of a "starter apartment". A starter apartment is the first apartment that a person can afford to buy. It's usually small and doesn't have many amenities. The hope is that one day the person will make more money or will have saved enough money to purchase a "dream apartment". The same idea exists for starter homes/dream homes.Suggestion:
son appartement temporaire
I agree with divishinating that "son premier appartement" doesn't really seem to imply the same thing as a "starter apartment" in English as I've explained above. Is there something that implies that this apartment is a stepping stone/launch pad to something bigger and better hopefully in the future?Bonjour!
"starter apartment" is literally "un premier achat immobilier" so your proposition is correct : "son premier appartement"