Quick answer: generally no for an ordinary sale to an unrelated buyer, once a personal representative has been appointed. But real property titled solely in the decedent's name can never be sold without that appointment happening first. Run your own numbers in the New Mexico probate real estate sale calculator.
Appointment comes first, always
A dispute sends the case to District Court
The Probate Court can only be used for simple proceedings. If a question arises about the heirs of the estate, who is entitled to the property, or the value of the property, the proceeding must be filed in District Court instead.
The deed itself needs care
A Personal Representative's Deed must be prepared, signed, acknowledged before a notary public, and properly recorded — the Probate Court doesn't prepare deeds, so the PR typically works with a title company or attorney to get this technical document right.
A 3-year window, with an exception for property transfers
In general, probate proceedings aren't allowed more than 3 years after a person's death — but there's an exception specifically for transferring property of the estate, which can still proceed under certain circumstances even beyond that window.
A local probate attorney can review your estate — many offer a free consultation.
Bernalillo County and Santa Fe County process these appointments through their own Probate Courts, but the rules apply identically statewide.