Genealogy / Need help with last name Hurkato [4]

So I have a little problem investigating my family. My great grandmother has the "Hurkato" (type in "Urkato" on the spanish google translate voice if you need to hear it) last name on all of her papers, however I can't seem to find any information on her. First name "Pelagia".

She was born in 1907 in Slowita, Lwow (now Ukraine, I think it has something to do with a pact between the two big neighbours signed in august 1939 and the collapse of the eastern one, I'd appreciate some data of who was in control of the country since I am attempting to apply for a citizenship), according to the papers I currently have at least.

Yes I have investigated ancestry.com, familysearch, and Ellis Island is not an option since I'm from Argentina and I doubt the lady took the trouble to go first to the USA then to Argentina when she got pregnant.

Full name is Pelagia Hurkato (as shown in the papers I have). I'm also searching for any birth records, I've contacted St. George's Cathedral (I don't know about Poland but in those times it was not uncommon for the church to be the one in charge of birth certificates and all that here in Argentina, if it was some other institution please let me know) in an effort to check if they or any of the smaller churches have the birth information. I understand that there is a chance that they were destroyed in the war but I'm hoping they have them.

I appreciate any help and apologize if it turns out that I looked in the wrong sites or I didn't look correctly.