Yes, you can file and claim the 2019 and 2020 stimulus packages.
TurboTax Free File will let you file your federal and state return at no charge as long as you meet the qualifications.
Here is how you will report that you did not receive the stimulus payments:
At the top of your tax return select Federal Review
That will take you to this screen where it asks if you have already received your stimulus payments. If you received the first or second payment already, then select Yes and fill in the information. If you did not receive any payment select No. If you received the first payment only, fill in that amount and put zero (0) for the second payment.
When the screen is correct, you refund will be adjusted for the amount of stimulus payment that will be added to your 2020 refund.