Autism Family Caregivers Act of 2023 This bill establishes a pilot program to provide training for caregivers on improving the well-being of children with autism spectrum disorder and other developmental disabilities or delays. To carry out the program, the Health Resources and Services Administration (HRSA) must award grants to, among other eligible entities, health systems and nonprofits to provide the training. HRSA must also establish a national center to provide technical assistance to grant recipients and to evaluate the program.