I am sorry for your loss.
While the trust was still revocable (your father was living and reporting it under his SSN), it was a grantor trust and not an entity separate and apart from your father (i.e., he was the "owner" of the assets in the trust).
When your father passed, the trust became a separate entity with its own tax ID number (EIN) and would have been required to file a 1041 if it had any taxable income for the tax year (or gross income of $600 or more).
The beginning date of this irrevocable trust with its own EIN would be the date of your father's passing.
The final return would be due by the 15th day of the 4th month following the close of the tax year, the close of the tax year being the date the trust was terminated, which could very well be a short year.
See https://www.irs.gov/instructions/i1041#en_US_2024_publink1000285977
