On the way to the basement garbage dumpster, the inmate fled on Harriet Alley in the direction of Harrison Street.
During his escape, Santiago-Gonzales took off his orange jail jumpsuit and was last seen only in his boxer shorts.
The deputy chased the inmate but was not able to apprehend him, according to the sheriff's department.
Other deputies and officers from the San Francisco Police Department have responded to aid in the search.
"From what little we know, he probably should not have been in the outside worker capacity," San Francisco County Undersheriff Federico Rocha told KTVU Tuesday morning. "Clearly this person could represent a danger to law enforcement or the public."
Last June, inmate Timothy Midgett disappeared from the same jail for 10 days after taking out the trash. His escape was supposed to prompt wholesale changes in how trustee inmates are managed.
"We did do a wholesale scrub of our procedures and policies to take those steps which we felt would secure the inmate, whether they're inside workers or outside workers," said Rocha. "Whether or not any or part of those procedures were violated... remains to be uncovered in the internal investigation."
Gonzalez was due for an April 7th plea deal meeting with federal prosecutors and was facing a significant amount of prison time. His attorney told KTVU he'd not shown signs of discomfort in jail or indications that he was planning an escape.
"I didn't feel that he had any erratic behavior or I would've called it to the attention of the authorities," said attorney Michael Stepanian. "He's not a threatening, violent person. He would more likely than not surrender on his own if he were to be trapped."