A CE750 crew departed on the TEB 5 SID and then climbed to 2000 ft before the 4.5 DME. The sun was distracting the Captain and 1500 ft was not used to alert about remaining lower until cleared on the SID.

Narrative

Prior to departure; Captain briefed TEB 5 departure. We were to depart Runway 24. Departure stated climb to 1500 ft turn to 280 degree heading and maintain 1500 ft until 4.5 DME; then climb to 2000 ft. I input information into FMC and Captain requested that I put the final level off altitude of 2000 ft in altitude alerter. Captain verified departure runway and altitude. After departure; sun was directly affecting Captain's vision and I attempted to put my sun visor in Captain windscreen to block excessive sun glare. I was not able to focus on Captain's altitude as my attention was focused on helping the Captain see. After placing the visor in front of the Captain's windscreen; ATC called us to inform us frequency change and notified us 'in future departures please maintain 1500 ft until 4.5 DME.' At that time; both Captain and I looked down at aircraft altitude and noticed deviation. At this time; we acknowledged deviation to ATC and switched to new assigned frequency. Next time; I will insist and ensure that the first level off altitude will be placed in altitude alerter and suggest to have appropriate pilot's sun visor placed in position when flying directly into a sun glare.