This is my first time filing taxes with turbotax how soon should I expect my second stimulus check

TurboTax cannot tell you if or when you will receive your stimulus check which will be issued by the IRS.  If you did not receive your stimulus check in 2020 and you are using the recovery rebate credit to get it, you will get the stimulus money with your 2020 income tax refund. 

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—if you are eligible.It will end up on line 30 of your 2020 Form 1040.

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

https://www.irs.gov/coronavirus/coronavirus-tax-relief-and-economic-impact-payments-for-individuals-and-families

https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-me/00/1393859

good post with screen shots for recovery rebate credit

https://ttlc.intuit.com/community/taxes/discussion/filed-as-an-independent-and-single-but-haven-t-received-either-stimulus-checks-will-i-ever-get-any/00/1781494

Did you e-file?  Did you click that big orange button that said “Transmit my returns now?”  If so, your return is now in “pending” on a server.  Do not try to change anything while your return is in pending.

First your e-file is going to sit on the server until the end of January when the IRS begins to accept/reject 2020 returns. anything while your return is.   Watch your emails so you will know by then if your return is accepted or rejected.   If accepted, they try to process it within three weeks but it can be longer.  if you have earned income credit or additional child tax credit, it will be at least the end of February before you see your refund, due to the PATH act that requires that they hold your refund longer.

Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 34of your 2020 Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others

If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.

https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

https://ttlc.intuit.com/questions/2724106-my-return-is-accepted-but-still-not-approved-is-there-a-problem-should-i-be-worried

https://ttlc.intuit.com/questions/3397970-path-act-delayed-refunds-for-some-filers