I believe the acronym CG (or alternatively “C.G.”) stands for “Centro de Gobierno (Municipal)”, but not being Salvadorian myself, I have my legitimate doubts about my proposal, doubts that justify my low confidence level.

This first reference is reliable (certainly as far as the content is concerned):
https://www.sanmiguel.gob.sv/tramites/registro-estado-famili...
ALCALDÍA DE SAN MIGUEL
REGISTRO DEL ESTADO FAMILIAR
Horario de Atención al Público
Centro de Gobierno Municipal

This second one is less reliable, but confirms what you guess and I also suspect, i.e. that “CG” means “Centro de Gobierno” (however, the context might be different, so careful):
https://migenteinformagt.com/miguel-martinez-del-centro-de-g...
(…)
XXXXX, el preferido del presidente YYYYY, logró copar el poder. Desde comienzos del gobierno le fue creado un centro de control y mando, que la administración decidió llamar el Centro de Gobierno (CG).

I have not found any Salvadorian web site in English which confirms my suggestion. This reference is Puerto Rican:
https://caguas.gov.pr/wp-content/uploads/2021/08/Avisos-Vist...
The draft of the 2020-2021 CAPER will be available to the general public from August 25, 2021 through September 15, 2021, 8:30am-4:00pm at the Planning Office, suite 301 of the Caguas Municipal Government Center, before its presentation to the Federal agency for evaluation and comments.

In documents issued by the Civil Registry of Ecuador, CG means the Office of the General Comptroller or Comptrollership