How do I get the second and third stimulus checks if there was not a choice to claim them?

If you are eligible to receive the 2nd check the recovery rebate credit section will allow you to enter information.   There is no place at all to enter anything about the 3rd stimulus check on your 2020 return.  The IRS is issuing those checks in phases on its own timetable.

The stimulus check is an advance on a credit you can receive on your 2020 tax return.  If something went wrong or you did not get the stimulus check in 2020, you can get it when you file your 2020 return in early 2021

The Recovery Rebate Credit will be found in the FEDERAL REVIEW section. ( you should see "Let's make sure you got the right stimulus amount”)  If you are eligible it will end up on line 30 of your 2020 Form 1040.

Make sure that you enter ALL of the stimulus money received for the 1st and 2nd stimulus for yourself, your spouse and your children.

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-j-reconciling-on-your-2020-tax-return

https://ttlc.intuit.com/questions/1901539-how-do-i-preview-my-turbotax-online-return-before-filing

Click on Tax Tools on the left side of the screen. Click on Tools. Click on View Tax Summary. Click on Preview my 1040 on the left side of the screen.