First Officer reported aircraft failed to pressurize on take off and discovered the air conditioning pack switches were left in the off position. Flight Crew descended and turned switches to the on position and continued the flight to destination airport.

Narrative

Morning flight out of ZZZ; [Aircraft X]. Captain Pilot Monitoring; First Officer Pilot Flying. Standard morning with no complications departing ZZZ. Climbing through 10;000 feet; we noticed the cabin pressure was higher than normal but within limitations. We reached 14;000 feet (final cruise altitude); and were immediately told to descend down to 10;000 feet. We set cruise props; and began our descent. Descending through 13;000 feet 'Master Warning; Cabin Press' illuminated. We donned our oxygen masks and ran the IAC checklist. Requested lowest sector altitude simultaneously; ATC cleared us to 9;000 feet. Before we finished the checklist Cabin Press Warning light extinguished. Despite this we kept oxygen masks on; and performed the pressurization fail checklist. We then were handed to ZZZ approach and requested lowest altitude; we were then approved down to 6;000 feet. Explained that we had an issue with pressurization and wanted the lowest altitude; but didn't require assistance. Continuing the checklists it was discovered the PACKs were in the off position. I turned the PACKs on and finished checklist. We removed our oxygen masks; and continued with the flight to ZZZ1. Called dispatch and advised of situation; and that all was normal now. Notified flight attendants; who said they didn't notice anything abnormal. Completed flight; landing safely in ZZZ1. Contacted Dispatch upon competing the parking checklist; and spoke with Maintenance Control. Decided to write up the event in the logbook.The PACKs being left off caused the incident. The potential addition of a separate line to verify PACK switch position on the originating or before start checklist could have mitigated the threat. Otherwise no other feedback is needed in my opinion.