By the time you get your baggage collected and through customs/immigration and get to the car rental office, you will probably be looking at rush hour. You are kinda between a rock and a hard spot because if you stay near the airport, you will be in morning rush hour the next day. What day of the week will you be arriving?

If you want to try to get out of LA that afternoon/evening, I'd try to get completely out of the valley - perhaps to the Hesperia/Victorville area. That's about 100 miles from LAX via 105/605/210/15. This could possibly take several hours. If you get out early enough and beat the worst of the traffic, you could try to make it to Barstow. The closer to LA you are, the rougher the morning traffic will be.

I would look at a European consolidator such as carhire3000.com for getting the best rental rate. I would make sure that whatever company you go with has an airport shuttle.

Another option would be to take a shuttle to a near-airport hotel, then pick up the car the next morning and wait till rush hour is mostly over before leaving. This would not get you to the GC before sunset though.

Victorville to the GC is about 7 hours.