at the present time your return is being held on a TT server to submit to the IRS when it opens e-filing on 2/12/21. until your return is submitted to the IRS there is no way to know if someone else claimed the child. it may well depend on whether your return hits the IRS computers before anyone else's who might have claimed the child.
The only way you'd be aware if someone has claimed your children on their return is if your electronically-filed return is rejected because of it. Mike 9241 above is correct.
You'd receive E-file reject R0000-507-01, since the IRS doesn't allow a dependent to be claimed on more than one return.
Please see the TurboTax Help article “E-file reject R0000-507-01: A dependent on your return has already been claimed (or claimed themselv...” for more information.
to clarify if you file first your return will be accepted. the other taxpayer's return claiming the same dependent(s) will be rejected and they will have to mail it in. you will not be notified of this. at some point both of you will get an IRS letter requesting each to amend to take off the dependents. this is when you'll first know someone else claimed one or more of your dependents. if neither amends there is a second letter asking each to provide proof that they are the one entitled to claim the dependents. the one that provides the stronger proof gets to keep them. the other gets a bill.