Susac (back) began a rehab assignment with Triple-A Sacramento on Thursday, going 0-for-3 with a strikeout.
Susac has been shelved for the past two weeks with a lower-back strain. He was used at designated hitter in his first rehab contest, and the Giants will surely want him to play at least a game or two at catcher before returning the rookie to the active roster, which could happen immediately after the All-Star break.