PC-12 Captain reported the Bleed Air switch was positioned incorrectly and led to a failure to pressurize on climb. The Captain reviewed the procedures; repositioned the Bleed Air switch correctly; and fully restored the systems.

Narrative

Bleed Air Valve was in the incorrect position; and a CAS message for ACS Low Inflow came on. During the troubleshooting process; I asked for a block 10;000 ft. to 12;000 ft. and was cleared for it by ATC. I leveled at 11;000 ft. and was beginning to descend back to 10;000 ft.; but not before the cabin altitude exceeded 10;400 ft. and the cabin altitude alarm came on. I became fixated on getting the alarm to turn off and initiated a descent that caused me to dip below 10;000 ft.; at which time the controller cleared me to 8;000 ft.It took me a while to realize I could silence the alarm by associating the Master Warning switch. The glare from the sun made it hard to see the light was flashing; but I finally remembered descending back through 10;400 ft. I had also briefed the passengers but failed to switch back over to ATC; so when I responded; Aircraft X cleared to 8;000 ft.;' he didn't hear me. I caught my mistake and switched back to COM1 from the intercom; acknowledged my new clearance; and asked for a block from 8;000 ft. to 10;000 ft.; which was then given. I continued to troubleshoot; and realized that the Bleed Air switch was now in the OFF position...when I was expecting it to be in the ON position. I turned the switch to the ON position and all systems began to function normally. I informed ATC that my systems were functioning properly now and that I was ready to continue my climb. Initially the controller wanted to know if I was sure I wanted to climb; and I assured him that the aircraft was good to go. The flight proceeded without further incident.To prevent this from happening again. I need to slow down enough to identify the position of the Bleed Air switch when I get the ACS Low Inflow CAS alert. I'm pretty sure that the system was never turned on and that when I followed the first 2 steps of the checklist; 1. ACS Bleed Air switch INHIBIT; [and] 2. ACS Bleed Air Switch AUTO; I actually flipped the switch from Inhibit to Auto; and back to Inhibit. Secondly; when I was trying to get the alarm to turn off; I needed to associate and push the Master Warning button right away to silence the alarm. The silencing of the alarm would have freed up enough gray cells to level at 10;000 ft.; switch over to COM1; and request the lower block in a timely manner. Finally; I need to do a better job backing up my flow with my Takeoff Climb Checklist and confirm the items line by line. This would have avoided the situation altogether as the ACS switch is one of the items."