How might one go about getting a baptism record for a person born in San Diego in 1973?
The name of at least one family Catholic church is known.
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Most churches will follow vital record laws, you will need the persons death record or their birth record along with their permission to obtain the baptism record. After you have that, then you can just start calling churches. There is no online database mostly because institutions are not allowed to give out birth records of people who are alive or born in the last 70 years.
Note: For the catholic churches in my area New Jersey, you can call the Archdiocese for more info. I would assume the same in the San Diego area.