Los Angeles Birth & Death: Torres

Hello All,
I have reached a road block with some of my research. I cannot find a birth record for my grandfather or the death record for his mother. The family story is that shortly after my grandfather was born in Los Angeles County in April 1926, his mother (Francisca Garcia) passed away August 1926. We do not know what from.

We have no records for her (death) or for him (birth). We do not know at this point where our great grandmother is even buried. There are confused records in the LDS. A member appears to have submitted incorrect data and the trail is lost until we find documentation tracing back to the correct location in Mexico. I do have a church marriage record for her but it has very little info on it.

For my grandfather, I've located one record of birth for a sibling born before him in L.A. by midwife. But he was not ever able to get his own.

I've made requests to the Los Angeles County and am also waiting to hear back from the state. Does anyone have any tips for how else I might find a lead? Is there a reason why records from 1926 in L.A. might be spotty?

Thank you,
Esperanza