Congratulations.
First, you need the child's social security number. If you can't get it from the mother's family and you don't have it with her important papers, you can contact the social security administration for help. You can't claim tax benefits without the SSN.
Next, you generally must have actual physical custody of your child more than half the nights of the year to claim her as a dependent (plus some other rules in the publications linked by the other experts). For 2021, it may be that she was in the custody of her mother for more than half the year before she died; in that case, the child can still be claimed as a dependent on her mother's final tax return for 2021. There is a provision that could allow you to claim her as a dependent for 2021 under a "multiple support agreement" as long as you provided at least 10% of her support and everyone else who provided 10% of her support signs a letter agreeing that you can claim her. But this is uncommon.
You can certainly start claiming her as a dependent in 2022 as long as you continue to have custody; whether you can claim her for 2021 depends on when she entered your home.
Under the current tax law, if you claim your child as a dependent next year on your 2022 tax return and you don’t change your withholding at your job, you would get a $2000 larger refund than you have been getting before. If you want to get that money in your weekly paycheck instead of as a lump sum at the end of the year, you may fill out a new W-4 form at your job.
I can't think of anything else critical you need to know now, but we will be happy to answer your follow up questions after you have digested this.
