Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Engineer
Flight Crew Last 90 Days 50; Flight Crew Total 28600; Flight Crew Type 3000
Situational Awareness; Distraction
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors; Procedure
I was the PNF on this leg.  The Captain was in the cockpit and started the right engine while I loaded equipment on board.  I closed the main cabin door and briefed the passengers.  This was their second leg with us so the briefing was abbreviated since a full briefing was given on the prior leg.  I was in a COVID mask and it was warm outside (82 degrees).  After the load I entered the cockpit and strapped in.  I received a briefing on the clearance and we started the left engine.  I was a bit rushed and I didn't review the departure procedure plate as thoroughly as I should have.  We departed [Runway] XXR and I didn't hear or the captain didn't call for me to select NAV on the MCP.  Therefore; we were late to make the required right turn to 025 degrees.  The Tower asked us to begin the turn.  I was rushed; hot and distracted by the COVID mask a bit.  I should have prompted the NAV selection if the Captain didn't call for it.  This was not a DP where there is a complicated course.  It is RNAV but basically a heading to a vector.  The heading change was subtle and I reviewed the DP in a hurry.
Air taxi First Officer reported a track heading deviation during departure.