No. A gift given in 2021 is not a gift for 2020. If you want to give the gift in 2020 then give them the money IN 2020.
Money that you receive as a gift is not taxable income to you, and you do not need to report it on your income tax return. Money that you gave as a gift to someone else is not deductible for your taxes.
Turbo Tax does not support the gift tax form 709, but here is a link:
So give them 15,000 at the end of December 2020 and then 15,000 in January 2021. Or are you married or are they? You can give each person 15,000 and if you are married your spouse can give someone 15,000. So a married couple could give another married couple a total of 60,000.