Another option is to drive down to Dumbarton Bridge and take 880N although I'm not sure how much time it would save you during the morning peak hours.

BART is your best bet. However, I'm not sure if you'd make the 7:52 train since your flight arrives at 7:40 considering you need to walk from the gate to the train to take to BART station.

You will probably be in Berkeley a little past 9am. If you are going to downtown Berkeley, take the dublin pleasanton train and transfer at Lake Merrit station to take the Richmond Train. Or, if you are traveling from Mon-Sat, you can transfer at any station before you cross the bay (past Daly city) to transfer to Richmond train. If you are going to Berkeley closer to rockridge, you need to still take dublin pleasanton train and transfer after Daly city to take the Pittsburg Bay Point train.