The first Anza Expedition of 1775 brought some of the first Spanish-speaking colonists into Alta California. At least one baby was born en route. Did Anza or anyone else in his party write down everyone's names?
Yes. The list of families is available on the U.S. National Park Service's website at: https://www.nps.gov/juba/learn/historyculture/people.htm. A note at the bottom indicates "*This list is adapted and does not include the Indian guides, vaqueros, mulateers, servants, and other members of the Anza Expedition of 1775-76 (including Father Font and Anza himself)."
A more comprehensive list is available in the diaries he kept for all the expeditions. You can read those in Spanish as well as translated into English on the University of Oregon's Anza project website at: http://anza.uoregon.edu/siteindex.html.