Father recently died, he has a will, but his witnesses died years ago

Dead witnesses are no problem.  The statute deals with this.  There is a proceeding that your lawyer needs to bring.  You need to prove the death of the witnesses by having the death certificates.  The affidavit of their son is not sufficient.  There is only one way to deal with this under the statute.  If your lawyer does not know, get a new one.

Unless the lawyer who prepared your father's will included a self-proving affidavit and the rest of the will was properly drafted and executed, nothing is cut and dry. If a lawyer drafted and supervised the execution of the will, ask your current lawyer if the drafting lawyer was located and provided an attorney affirmation of regularity, which should expedite probate. However, even that lawyer may be subject to a hearing before letters are issued- ask your attorney that question, as well. Even when the file is complete, unless the petition for letters testamentary was filed with an affirmation of urgency, depending on the county, Surrogates Courts take a long time to issue letters.