Any of these might work:
1a) Find her death certificate / record.
1b) Find her obituary. It may not have her maiden name, but if Mary Rogers is survived by brothers Albert Smith of Abeline, Bruce Smith of Beloit and Charles Smith of Cincinnati, you've got it anyway.
2) Find her cemetery records.
3) Buy her SSN application.
4a) Find her marriage record.
4b) Find an article about the wedding in an old newspaper.
5) Find her in the US census with a relative - preferably father-in-law - living with her and her husband; a brother, if she is head of household, or brother-in-law if her husband is still alive, would probably be it, but if her husband's sister's husband is with them, B-in-L may be misleading.
6) Find a birth certificate / record for any of her children.
7) Find her and her husband living with her parents in their early years in the census.
All of these assume she was born and lived in the USA.
The middle years are not much good for maiden names on censuses, but people in their teens and twenties, just married, sometimes lived with the wife's folks. When the parents got into their 60's they sometimes moved in with their adult children. Those census entries can sometimes give you three generations at a whack, and are pure gold.
> I'm trying so hard to find out her giving name at birth
GIVEN name is also "first name" or "Christian name". The surname (last name) she was born with is her maiden name.
If she was given the name "Bethsheba" at birth, hated it and changed to "Mary" as soon as she ran away from home at 14 to join the circus, you'll never find it.
