Sunday AM connections?

I wonder who serves the people who are about on a Sunday morning?

Generally, the vast majority of Christians are either in a church service or sleeping in (one of the great reasons to attend later in the afternoon/evening).

Who is being the Christian witness to all the families who spend Sunday morning down at the beach or at the park with their kids?

Sure, those people can and, in an ideal world, should be bumping into believers during the est of the week... but what about Sunday morning???

One idea, which I always thought was impractical, was to release a portion of your morning service to serve and make connections during "church time" on a Sunday. Could a church every, instead of having their building be full of young families, intentionally invite them to make connections in their community in this time frame?

Saddleback is doing a pretty good initiative along these lines this Sunday, as reported here.