You don't need tiny apartments to have density. You can do it with smaller single-family houses on smaller lots, narrow one-way streets, and alleyways for parking instead of driveways and garages. This is how the pre-war streetcar suburb of Riverdale, Toronto is designed [1] and it has much higher density than the rest of the city.
[1] https://www.youtube.com/watch?v=MWsGBRdK2N0