Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP)
Distraction; Time Pressure; Communication Breakdown
Airspace Violation All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
General None Reported / Taken
Human Factors
The day began with a maintenance delay. In ZZZ XXX Radio issued us a Hold For Release Clearance about 15 minutes prior to departure. I read the clearance back and wrote down 'HFR' at the bottom of my clearance.Once bag loading was complete we started engines taxied; and took off.  After takeoff XXX Radio called us and asked if we had departed.  We then realized we had not gotten ATC release.  Nothing further.Keep the pacing normal; no need to rush.Develop a technique to remind you that you do not have takeoff clearance.On the next leg we also had a Hold For Release clearance and I put the checklist between the throttles to remind me and verbally repeated 'Hold For Release' on every radio call on CTAF frequency.
We were running late due to an FMC issue in ZZZ and trying to make up time.  XXX radio said they would issue us a hold for release time when we had a better idea when we would be taking off.  We finished up with loading; engine start and check lists.  We took off and before we reported in with ZZZZ radar XXX called and asked when we would be taking off.  We explained that we had forgotten to get the hold for release time and were enroute.  They activated our flight plan and we proceeded without event.  They gave us a phone number for ZZZZ and we called reaching ZZZ1.I had not flown in 6 months due to the pandemic.  In the future I will go slower and put out a visual reminder when ever issued a hold for release; such as a QRC between the throttles.
Air Carrier flight crew reported taking off without an ATC clearance. Captain reported having not flown in 6 months.