does the management allow you to put the flyers under doors? If so, like someone said, make it as an invite to an event like when CA meets in the park.
Back when I lived in a appartment, I became like the area organizer by promoting things like a clean up the area event that included a nearby park and nearby neighborhood or put together a appartment complex pot luck or adult swim party. Once in awhile I would include tracks with the other flyers I put under people’s doors – with a promise not to push religion on them at the parties.