Head of Household and Claimed Dependent

I am the residential parent and it is the other parents year to claim our child for the 2024 tax year. I completed my taxes first as Head of Household and the other parent tried to claim our child as a dependent but received an error of some sort stating someone else claimed our child. Did this happen because I filed first as head of household or is it a separate possibility? I spoke with the IRS and there was no flag/fraud tied to my child’s SSN. (Both parents are not together, never married and do not live together)