I never filed an income tax return before. Can I claim a premium tax credit this year?

Yes in most cases. People who have not filed a tax return before can qualify for a premium tax credit. However, there is a requirement to file a return for the tax year in which you receive a premium tax credit.  If you got an advanced premium tax credit last year, you must file a federal income tax return for that year to be eligible to receive an advance premium tax credit next year.