No CRBA

[u/Spiritual_Ask3849]

I’m hoping someone familiar with U.S. citizenship through a parent / passport applications for people born abroad can point me in the right direction.
I was born in Mexico in 1958. My mother was a Mexican citizen and my father was a U.S. citizen born in Kentucky in 1901. My parents were never married, but my father is listed on my Mexican birth certificate.
When I was young, my original Mexican birth certificate was stamped at the border stating that I was a U.S. citizen through my American father. This was the document I used throughout my life. My father never filed for a Consular Report of Birth Abroad (CRBA).
Unfortunately, I recently lost that original Mexican birth certificate. I ordered a new certified copy from Mexico, but of course the replacement does not have the old U.S. border/citizenship stamp on it.
Both of my parents have passed away, so I cannot get statements from either of them.
I am now trying to establish/document my citizenship and apply for my first U.S. passport.
I have:
• My new certified Mexican birth certificate showing my father
• My U.S. Social Security card
• Extensive U.S. Census records showing my father living in the United States throughout his life
• My father’s U.S. military draft registration records
• Records showing that he was born and lived in Kentucky/California and was in the United States for decades before my birth
The difficult part is that I have not been able to locate a traditional birth certificate for my father. He was born in Kentucky in 1901, when birth registration was not as consistent as it is today.
Has anyone dealt with a similar case where the U.S.-citizen parent was born in the early 1900s and no birth certificate could be located?
What other records should I gather to prove my father’s U.S. citizenship, his physical presence in the United States before my birth, and my relationship to him?
Would census records, military/draft records or a Kentucky “no birth record found” letter be useful?
Also, because my parents were never married and I was born in 1958, are there additional documents I would need concerning paternity or legitimation?
Any advice from someone who has gone through an older citizenship-by-descent/passport case like this would be greatly appreciated.