Promoting Access to Broadband Act of 2023 This bill establishes grant programs to facilitate enrollment in the Lifeline program and the Affordable Connectivity Program. (These programs subsidize telecommunications services for eligible, low-income individuals and households.) Specifically, the Federal Communications Commission (FCC) must award competitive grants to states, territories, or tribes for informing Medicaid enrollees, recipients of Supplemental Nutrition Assistance Program benefits, and other low-income individuals about their potential eligibility for the programs. The FCC must also award grants to states, territories, and tribes to facilitate data sharing for verifying eligibility for the programs. Recipients must use the grants to establish or maintain connections between (1) their databases that contain information about residents who receive benefits administered by the recipient, and (2) the National Lifeline Eligibility Verifier (a centralized system that verifies and annually recertifies Lifeline applicants' eligibility for the program).