Advancing Health Savings Act of 2023 This bill excludes from taxable income any distributions from a health savings account (HSA) used to pay qualified medical expenses incurred before the HSA is established if the HSA is established within 60 days from the first day of coverage under a high-deductible health plan (HDHP). Under current law, distributions from an HSA established in connection with a HDHP are excluded from taxable income if used to pay qualified medical expenses incurred on or after the date that the HSA is established. However, under current law, HSA distributions are taxable if used to pay otherwise qualified medical expenses incurred after enrolling in an HDHP but before establishing an HSA. Under the bill, an HSA that is established within 60 days of the first day of coverage under an HDHP is treated as being established on the first date that coverage begins under the HDHP.