Looking for a birth certificate

Hello, and apologies for posting in English as I cannot read/write Polish.

I am looking for the birth or marriage certificate of one Michał Marcol (or Michał Marcola), who I expect was born in Poland (possibly in Warsaw, or in Majdan Trzeszczański) around the year 1813 (+/- 3 years), so that I can figure out the name of his parents.

For additional background, he is the father of one Jan Marcola, was married to Helena Goźdź (probably around 1840), and was a farmer living in the village de Majdan Trzeszczański, as attested in the attached birth certificate of Jan Marcola which was very graciously sent to me by a member of this forum.

I was unsuccessful in finding Michał Marcola at https://geneteka.genealodzy.pl/index.php?op=se&lang=pol. I also checked on Minakowski’s Great Genealogy (https://wielcy.pl/) but the Marcola family tree stops at Michał and I am missing his parents’ names. I would like to seek your advice on where else to search, as I am not familiar with genealogical sources in Polish.

Many thanks in advance!