Yes. It is normal, and it normally takes 6 to 8 months after the I-360 is approved.
A competent attorney will know how to make a case specific inquiry on your behalf.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
What you haven't stated and is the first fact in circumstance is the U.S. immigration status of the original petitioner (widower, abuser, etc.). If they were an LPR then you may not receive an interview for some time. If they were a citizen, then I'd guide you to review the processing times for I-485 applications in San Francisco. These can be found on the USCIS website.
4 months isn't a long time to be waiting .. be patient.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship.