Date: 202003
Local time of day: 0601-1200
Location: ZZZZ.Tower, FO
Light: Daylight
Aircraft: Light Transport; Low Wing; 2 Turbojet Eng
Operator: Fractional
Operating under: Part 135
Flight plan: IFR
Flight phase: Taxi
ATC / advisory: Center ZZZZ
Reporter organization: Fractional
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Distraction; Confusion; Communication Breakdown; Troubleshooting; Situational Awareness
Second reporter function: Captain; Pilot Not Flying
Anomaly: ATC Issue All Types; Airspace Violation All Types; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway; Ground Incursion Taxiway
Detector: Person Air Traffic Control
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Airport; Environment - Non Weather Related; Human Factors; Procedure
Primary problem: Environment - Non Weather Related

Narrative: On the flight from ZZZZ to ZZZ; I picked up the clearance on ground and we were ready early. Passengers were early and after loading and starting; we couldn't contact anyone on Ground; Tower or Departure frequencies! Aircraft Y told us the Tower just closed. We switched to update the ATIS and sure enough Info Q said the Tower was shut down due to staffing issues. We talked with Aircraft Y landing on Runway X; he gave us the frequency for ZZZZ Center; while we self broadcast on Tower frequency that we were taxiing to Runway Y. Prior to takeoff; we again tried Ground; Tower and Departure frequencies! No answer! After Aircraft Y landed and cleared all runways; we broadcast in the blind on frequency and departed. Once airborne; we tried to contact Departure on frequency. No luck. We were VMC and maintained that until establishing contact with ZZZZ Center. After radio and radar contact was established; we were cleared to FL230. After about 30 miles; ZZZZ Center told us ZZZZ Tower called and reported we had an Unauthorized Departure!We tried again to contact them on the assigned frequency; No luck. We continued to ZZZ with normal radio contact the whole way. Unusual circumstances with the virus affecting operations. Tower shutdown after giving us our IFR clearance. There were only two airplanes flying at that time. Very strange circumstance.


Second narrative: On the flight from ZZZZ to ZZZ; The Captain picked up the clearance on the ground. When the passengers arrived early and after loading and starting; we couldn't contact anyone on Ground; Tower or Departure frequencies! An inbound Aircraft Y told us the Tower just closed to listen to the current ATIS. We switched to update the ATIS and sure enough Info Q said the Tower was shut down due to staffing issues. We talked with the Aircraft Y landing on Runway X on Tower frequency to coordinate his arrival with our departure on Runway Y; the Aircraft Y pilot also gave us the ZZZZ Center frequencies if we were headed towards ZZZZ. While we also self broadcast on Tower frequency that we were taxiing to Runway Y. At no time did anyone from the Tower intervene on frequency that we were using. The airport was technically at that point a uncontrolled field and we acted appropriately with proper radio calls and coordination with the inbound aircraft.Prior to takeoff; we again tried ground frequency; tower frequency and departure frequencies with No answer.After the Aircraft Y landed and called clear of runways we broadcast on Tower frequency and departed Runway Y. We made a right turn out over the island to avoid [Prohibited Area] and proceeded North.Once airborne; we tried to contact Departure on frequency. We were VMC and maintained that until establishing contact with ZZZZ Center. After radio and radar contact was established; we were cleared to FL230.After about 30 miles; ZZZZ Center told us ZZZZ Tower called and reported we had an Unauthorized  Departure!We tried again to contact them on their departure frequency; with No reply. We listened to the ATIS again and at XA:55z it was broadcasting the XB:00z ATIS with no mention of Tower closure. We continued to ZZZ with normal radio contact the whole way.


Synopsis: Pilots reported departing without clearance in what they thought was an uncontrolled airport resulting in runway incursion and airspace violations.