EMB ERJ 170/175 ER/LR
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Distraction; Time Pressure
Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Overcame Equipment Problem
Human Factors; Procedure
After waiting on the ramp in ZZZ to receive our clearance from ATC; the First Officer and I decided to taxi out and wait just like another airliner flight had done in front of us. We obtained clearance to taxi to Runway XX behind the other airliner. About 5 minutes later; as I approached the 737; I decided to shut down the number 2 engine since we still did not have our IFR clearance due to ATC computer issues. As soon as we shut down engine number 2; ATC issued the other airliner their IFR clearance. In the meantime; we had started the APU in order to shut down number 1; but it became unnecessary since we figured we would be issued our clearance right after the other airliner. Once ATC finished with other airliner; they called us. I instructed the First Officer to start engine number 2. Tower gave us takeoff clearance; but we replied we needed 2 minutes. First Officer and I reviewed our IFR clearance and re-briefed the departure.It is at this moment I am sure I set us up for failure. I forgot to call for an After Start Checklist. As a result; I never reset the TRS (Thrust Reference System) page in the MCDU after shutting down the number 2 engine. We had the EICAS caution message pop up ENG NO TAKEOFF DATA. I reviewed all my PFD indications and everything looked normal. I noticed our APU was still on and I confused the message with the ENG REF ECS DISAG. Since that message is so common; I reached up and turned off the APU knowing the QRH tells us the conditions for the message to be APU ON; REF ECS ON; Engines Idle. I have gone over the scenario multiple times in my head today and I believe the EICAS message did go away. We ran the Taxi Checklist and told Tower we were ready for departure. We ran the Before Takeoff Checklist. We lined up and took off. I don't recall seeing any EICAS message up during line up and my initial takeoff roll when I brought the throttles to TOGA; as I always do a quick check and then transition outside when I am pilot flying. After takeoff at 400 feet; I called heading and I noticed we had Pack 1 and 2 Off. I then thought maybe I bumped the throttles past TOGA. They were not past the detent. I believe I missed the TRS and we ended up with a default ECS OFF No Flex takeoff. I consider this to be a serious safety issue especially because the runway in ZZZ is short and there is already such a small margin of error. I hope to never make this mistake again and will exercise even more caution in the future.
E175 Captain reported not completing the After Start Checklist and taking off without the Thrust Reference System activated.