The State of California and the U.S. Department of Housing and Urban Development have released Homeless Management Information System data on a quarterly and annual (respectively) basis.
Homeless Data Integration System - California Interagency Council on Homelessness
People Receiving Homeless Response Services by Age, Race, Ethnicity, and Gender - Datasets - California Open Data
APR: Annual Performance Report
System Performance Measures
Point-in-Time (PIT) and Housing Inventory Count (HIC)
Annual Homeless Assessment Report (AHAR)