Yes, it is possible for a child to be a "qualifying child" for Earned Income Credit (EIC) purposes, even when you are not claiming them as a Dependent.
However, one of the qualifications the child must meet is that they lived with you more than half the year. So if your son and/or daughter did not live with you at least 183 days during the year, they would not be qualifying children for the purposes of EIC.
Check out the TurboTax FAQ below to review all of the qualifications a child must meet for EIC purposes:
https://ttlc.intuit.com/replies/4835245
