On the following page you will find general registers for civil status documents in Hamburg from 1876 onwards:
- Name register births 1876-1900
- Name register marriages 1876-1932
- Name register of deaths 1876-1983,
on the other hand name registers of the former Prussian registry offices, now belonging to Hamburg, from 1874/1876 onwards.
https://ahnen-forscher.com/kirchenbuecher-hamburg/
General register means that it contains all entries in the Hamburg registry offices cataloged with the indication in which registry office the official act took place. In a separate folder you will then find the signature where these can be found in the Hamburg State Archives. All links are deposited with pdf-files (Attention these are often over 100 MB large)
You can also go directly to the page of the city of Hamburg:
https://www.hamburg.de/bkm/digitalisate/
Also the Hamburg Lutheran church records from 1816-1866 are stored in the State Archives and under the link you can also find there corresponding general registers (fonds 322-2)