Your post is confusing but I will take a stab at it ...
1) other parent claimed the child on the 2020 return ... if they were supposed to then there is nothing to be done.
2) their refund was not grabbed for an offset of child support ... maybe they did not have a refund OR their return has not been processed yet OR the offset has not been released yet for distribution (this can take 6 months or more depending on the state)
3) if the child lives with you for more than 1/2 the tax year 2021 then you will claim them on the 2021 return to get the CTC
4) you may be able to get the CTC advance when they open the portal sometime over the next month ...
For more information, see the following links on the IRS web site.
Jan 1 of what year - 2020 or 2021?
If she lived with you more than half of 2020, then only you could claim her unless you release her to the other parent with a 8332 form. If Jan of 2021 then 2020 is over with and you claim her in 2021.
If you or a dependent that you are entitled to claim has already been claimed by another taxpayer, your e-filed return will reject since the SSN has already been used (either intentionally or in error such as a mistyped SSN).
Your only recourse is to file a correct tax return, claiming what you are entitled to claim, then print and mail the return.
The IRS will process both returns and pay any refunds. Shortly (within a year) the IRS will mail letters to both taxpayers asking if their tax return was filed in error and suggesting that they amend if they improperly claimed.
If neither taxpayer amends, the IRS will send a second letter asking for each taxpayers proof that they are entitled to the claim.
The IRS will evaluate each taxpayers claim and award the credit to one taxpayer, the other will have to payback any refund received plus interest and possible penalties.
Do not ignore the letters or you will loose.