Hello,
as mentioned above, it is likely that your great-grandfather's birth record has not survived but don’t give up hope just yet. The main records were kept at the St. Nicolai Parish and were destroyed when the church was gutted in 1944 (not 1943) because of an air raid. The duplicates that each parish had to keep are held by the archives in Detmold. They were digitized and uploaded via Archion to serve as a makeshift replacement. Unfortunately, they are very inconsistent but I came across the following note:
http://www.archion.de/p/1cb51b54d5/. The respective digital copy only contains those years that are not marked with "besch.". I assume that this abbreviation means "beschädigt" (i.e. "damaged") so the respective pages might not have been included because they were too fragile for digitization, yet they might still exist. Therefore, there is a slight chance that those pages are still kept at the archives in Detmold. As the note also applies to the birth records of 1872, the year your great-grandfather was born, I suggest you write to the archives (owl@lav.nrw.de) and ask for the whereabouts of the duplicates of the birth records for Bielefeld-Altstadt (St. Nicolai) of 1872. Tell them the signature P 1 B Nr. 40 (because P 1 B indeed refers to the signature of the duplicates that are kept at the archives in Detmold like Paul-Reinhard has pointed out, cf.
https://www.archive.nrw.de/LAV_NRW/jsp/bestand.jsp?archivNr=409&tektId=1310&expandId=1309). I wish you the best of luck!
In case the record cannot be retrieved, you can still try something else. Do you know your great-grandfather's marriage and/or death date? If you do, you can write to the municipal archive of the city of Bielefeld (
[URL]https://www.stadtarchiv-bielefeld.de/Kontakt)[/URL] and ask for the respective records from the register office. Even if you don’t know his marriage and death dates, you can give the staff his full name and birth date and ask them to look up his marriage and death records for you as the records have been indexed. It is likely that either one or both records contain his parents' names and maybe even more information about them. If you're lucky, his parents’ marriage record can be retrieved from the aforementioned duplicates. The municipal archive’s staff are very knowledgeable and usually willing to help, especially since you are too far away to do the research yourself. They also know if consulting additional sources like resident registers, house number lists, etc. could be worth a try.