If California were a nation state, it'd be ranked number 36 of the world's most populated countries. Yet for some reason nobody has looked at their very accessible and up to date birth data (at least not that I have seen).
January -October
Live Births YOY change
2018- 379,984
2019- 377,954. -0.5%
2020- 353,996. -6.4%
2021- 348,436. -1.6%
2022 - 347,964. -0.1%
https://data.chhs.ca.gov/dataset/test-cdph-statewide-live-birth-profiles
Note- 2022 data is provisional, meaning it may be incomplete. All other data are final.
In the US the number of births generally have been dropping 1- 2% per year. While I can not definitively explain the 2020 drop , my guess is there were fewer births by non-US residents during the COVID scare. This is an easy way to get your child citizenship, come to California while pregnant and deliver. Not much of that was happening during much of 2020. Plus you may have had some of the more affluent pregnant women who were residents who left the state to avoid Californias lockdowns
In any event, I see zero association between the vaccines and number of live births in California.
I provide the Monthly data below for reference
2018- 2019- 2020- 2021- 2022
Jan 38,260, 37,472, 36,036, 31,986, 34,543
Feb 34,551 37,373, 33,315, 30,096, 31,991
Mar 37,883, 37,226, 35,013, 34,649, 35,453
April 35,665 35,152, 33,263, 33,486, 32,595
May., 37,485, 37,439, 34,983, 34,373, 34,062
Jun 36,794, 35,719, 34,465, 34,385, 34,243
July 39,695, 39,329, 37,271, 36,481, 36,648
Aug. 41,243, 40,401, 37,204, 38,373, 37,895
Sep 39,234, 38,824, 36,457, 37,481, 35,864
Oct. 39,434, 39,422,35,989, 37,126, 34,670
As a sanctuary state for illegal immigration as well as a desirable destination for birthing tourism from countries like China, birth rates alone will not give you the full picture.
There was also the leaked letter from a Fresno hospital regarding the increase in stillbirths from 1-2/month to 20+ for August and already 8 mid-September.
https://www.theepochtimes.com/exclusive-leaked-hospital-memo-reveals-500-rise-in-stillbirths-fetal-specialist-explains-likely-cause-facts-matter_4834951.html