Discover Mom's Citizenship Date

I need help finding the date my mother became a US citizen. I don't have any documents, but I know the approximate time period.

Requirements:
- Experience with immigration and naturalization records
- Ability to conduct thorough research
- Access to relevant databases or archives
- Detail-oriented and reliable

Ideal Skills:
- Background in genealogy or history research
- Familiarity with US citizenship processes
- Strong investigative skills

Please provide a timeline and method for your search.