and gave them a 10 year time frame.
Of course they couldn't go through the records of a whole decade. Can you imagine how many children were born over ten years? The research would take weeks, if not months, and the archives are short on staff given the rising number of requests.
It would be hard to find out if was their first child or not. I probably should not focus on trying to find this out.
You have to. Otherwise you will never find the marriage record, because you don't know in what year the marriage happened and nobody in the archives would be willing to research over an undefined time frame (see above). Just give it a try. Maybe you are lucky and it was their first child. If not, ask the archive to check the previous year for another child of that couple. Go backwards until you find the first born (provided they were all born in the same parish).
But I do not know for sure because they moved, apparently, a lot of things into the archiwums.
There are certain restrictions before things like church books and civil registration records are publicly available. 100 years for birth records, if I recall correctly.
civil registration office... isn't that basically the archiwum?
No. State archives (archiwa.gov.pl/?CIDA=177) are like a libraries - collecting old documents, records and other stuff from all over the country, and making them available to the public. A civil registration office was introduced in most parts of Germany in October 1874. Some places a little earlier. From then on it was mandatory to register births, deaths and marriages, and people got married at both the church and the civil registration office. Poland continued with this practice after its independence.