No. There's no place to enter an age or date of birth on any form. Certainly not on the 1040. It has a place to enter the name, SSN, relationship, and whether that dependent qualifies for the child tax credit or for the credit for other dependents. The filer checks that based on eligibility criteria. I suppose the IRS could use the SSN to look up that person's age in the Social Security Administration's database, but I don't believe they do that. It's simply "eligible or not".
Here's the 2020 1040, but the 2019 is pretty much the same:
e-Filing will ask for a date of birth, but only for the filers and not the dependents. I understand that they check that against the SSA database and will reject the e-file if incorrect. Other than that I don't believe the IRS normally knows how old a dependent is. The only requirement for a child to receive the stimulus payment as a dependent was that they're eligible for the child tax credit. So it's either check that box or not.