The only thing I'd be worried about is that last BART ride to the airport. Does your cousin live near a BART station? Because BART starts running at 4, but the trains are still twenty minutes apart at that hour, I think, so if you miss the one you need, you could be in trouble. It's doable, but you're going to have to wake up really early!

And I would love to meet up, but that is tentatively a weekend I'll be up north visiting friends. I would still be free Thursday evening, though.