Once your taxes as accepted for processing, they cannot be changed. Come back in late March when the 1040-X amended return form is ready.
If your Form 1099-G is reporting unemployment compensation, then you will need to amend your return to include that taxable income.
If your Form 1099-G is reporting the amount of your 2019 state income tax refund and you used the standard deduction on your Federal return for 2019, then you will not need to amend your return.
If your Form 1099-G is reporting any other type of payment or income, then you will need to amend your return to determine if it is a taxable amount.
After the 2020 amended return forms have been released, the following TurboTax article will update with instructions for how to amend. In the meantime, you can register your email through the article to be notified when the forms are ready.
How do I amend my 2020 return?