You flew along the shore in front of LAX westbound departure?
I swam in the area once and saw helo fly along the beach.
I would say that westbound departing planes are at least a few thousand feet up by the time they hit the shore.
Yes, you can fly under the planes. It's called the shoreline route and is done by many private aircraft.
There is another route that let's you fly right over LAX north and southbound. This is the VFR corridor and is an amazing sight.