A full calendar can make a hire look like the obvious answer. Follow one late project through the team first. Note when someone was working on it and when it was waiting for input, review or correction.
Spare hours are not interchangeable
Three projects may wait for the same senior reviewer while other staff have time available. Another generalist could add more work to that review queue. Protecting review time or arranging qualified cover may address the immediate delay.
Timing matters too. Hours free on Friday cannot supply an approval needed on Tuesday.
Include the work outside projects
Management, proposals and supervision take time. A plan that assigns every contracted hour to delivery overstates what is available.
Separate confirmed projects from possible work. Ask what the new person would do and whether that would reduce the queue you found. The capacity worksheet helps record those assumptions.