Try to do this on Tuesday through Thursday
Leave so you won't hit the LA area until after 9AM, 10am is better. This will keep you out of the commuter traffic.
I-15 to I-10 to 710 freeway south to Long Beach. Long Beach is mostly a protected harbor but there are beaches south of the main part of the city.
Take the Ocean Bl exit and head south past downtown Long Beach. You'll find parking along Ocean and some parking lots.
To avoid traffic and see better beaches you might consider heading to Malibu or Ventura instead. These are more traditional California Beaches with less traffic and better parking options.
Do a Google search for Rincon Parkway in Ventura. This would be my choice. Besides camping spots there are lots of day use areas.