I assume that you meant to say that your father did not explicitly designate a beneficiary and that the estate was the beneficiary by default, not that the IRA had no beneficiary.
The estate cannot yet be closed since the estate still holds the inherited IRA for the benefit of the estate. As I said above, the IRS has permitted such an IRA to be transferred to separate inherited IRAs for the benefit of the respective estate beneficiaries. If the IRA is not transferred out of the estate, an estate banking account will have to be established to receive distributions from the IRA and the income from the IRA passed through to estate beneficiaries. As it the IRA is presently titled with the estate as beneficiary, distributions must be paid to the estate. They cannot be paid directly to estate beneficiaries unless the inherited IRA is transferred out of the estate to separate inherited IRAs for the benefit of the estate beneficiaries.
Unfortunately, the previous reference I provided that was authored by Natalie Choate no longer exists at the link that I provided above several years ago. See another reference that she has provided where she discusses on page 12 rulings where the IRS has permitted an IRA inherited by an estate or trust to be transferred to separate inherited IRAs for beneficiaries of the estate or trust: https://www.ataxplan.com/wp-content/uploads/2020/11/TrustAsBene-2020.pdf
