How long does it take to obtain a marriage certificate?

Not to worry, that "officer" was a square head, but there was no way he/she could have known what is needed for filing an "adjustment of status" (AOS) marriage-based green card application. While true what the "officer" told you, to file for AOS all you need initially is to submit the "courtesy copy" marriage receipt you will be receiving on the day of your marriage. Nothing else. All you'll need to do after that is to make sure to bring the "certified copy of the "long-form" marriage certificate to your green card application interview to be scheduled in downtown L.A. within 6 months of your AOS application. Feeling better now?

Yes, a courtesy copy is all you need.