Can an estate trustee sell a property before knowing the full extent of the deceased's debts?

Generally, yes, and it's often sensible to do so. Selling a property is different from distributing the proceeds to beneficiaries, and converting real estate into cash the estate holds is frequently a reasonable, even necessary, step even before all the deceased's debts are fully known, particularly where the property would otherwise sit vacant, depreciate, or generate ongoing carrying costs like insurance, utilities, and property tax that drain the estate while debts are being sorted out.

The real caution point is what happens after the sale, not the sale itself: an estate trustee who distributes all of the resulting proceeds to beneficiaries before reasonably confirming the estate's debts, including things like a tax clearance certificate confirming no outstanding tax liability, risks having to personally cover any shortfall if debts later turn out to exceed what remains. So a trustee can generally sell the property proactively, but should hold the proceeds, rather than paying everything out, until they've taken reasonable steps to identify and address what the estate actually owes. Anyone administering an estate with unresolved debts should get advice on timing the sale and the eventual distribution separately, rather than treating them as the same decision.