ERJ-170 First Officer reported diverting to an alternate airport after experiencing loss of cabin pressure.

Narrative

36-XX-XX-X ENG BLD SYS BLEED 1 MEL; 24-XX-XX-X ENGINE DRIVEN GENERATOR IDG 2 MEL.FL300 entered as initial cruse alt on MCDU; APU operated for entire flight. Normal system operations. From Gate to Cruise.Approximately XA:04 pm eastern we reached a cruising altitude of FL300. Several minutes later I heard a 'pop' (similar to a lavatory door closing in the forward LAV) I happened to look at the EICAS after and observed a cabin ALT of 6000 ft. and a climb rate of 300 ft/min. This normal indication turned into a climb rate of +600 ft./+800 ft. of cabin alt. After observing this abnormal indication I alerted the Captain and then the abnormal indication turned into a cabin alt climb of +800/+1000 ft. a min. We both realized that this was an abnormal indication and checked the ECS page on the Captains side of the aircraft. The Outflow valve was shown as completely closed and the cabin rate was still climbing. The cabin alt reached an Amber indication but still below 9700 alt. And the cabin rate of climb was still going up. The Captain initiated a descent and we both put on our oxygen masks and established communication with each other. I told ATC mistakenly and on my own 'that we had a rapid decompression issue; then shortly corrected that statement to a decompression issue and needed 10000 as a cruising alt' because the CABIN ALT Hi caution message was going to pop up. ATC immediately approved the request. We discussed leveling off at a higher cruising alt to see if we could hold pressurization at FL220 and I put it on request and as soon as I did it was approved and the CABIN ALT HI EICAS message popped up. I requested the original 10000 ft. and it was immediately approved ran the rest of the QRC since we already accomplished the memory item. Ran the QRH while monitoring the aircraft airspeed and alt. We leveled off at 10000. We told ATC souls on board and fuel in time. A cabin alt of 8000 ft. could be maintained by the pressurization system. So we [advised ATC] and told ATC that the masks didn't drop. We knew we were over ZZZ and continued under ATC vectors south of ZZZ (relatively on course for ZZZ1). Sent an ACARS Message to Dispatch telling them decompression at FL300 now at 10000 ft. over ZZZ with FOB XX.X. We then tried to contact Dispatch over ARINC frequency; but we received an ACARS message to divert to ZZZ from Dispatch before we could contact them over ARINC. We told ATC of our intentions to go to ZZZ. Got a left turn and joined a 30 mile final for Runway XXR at ZZZ. We landed there and were assigned a new aircraft to continue our flight to ZZZ1. We did continue the flight from ZZZ to ZZZ1 with the new aircraft. Hazard would have happened to anyone. Very possible that if we didn't start our descent when we did; the masks would have dropped in the back. Monitor the EICAS like we did.