A321 Captain reported an engine starter warning during push back and engine start. The Captain improperly responded to the ECAM and immediately applied braking and shut down the engine to regain control of the aircraft.

Narrative

During pushback from [Gate] XX our ground crew gave me the clearance to start engines. I told my First Officer (FO) to start number one; as the engine accelerated we got an ECAM; ENG 1 START FAULT. THRUST LEVER NOT AT IDLE. THRUST LEVER…IDLE. I Momentarily followed the ECAM and moved the thrust levers to idle but then moved them both to the climb detent in a moment of confusion! Before I could gather my thoughts the engine began accelerating; I stepped on the brakes pulling both thrust levers back to idle and turned off engine 1 master switch. I immediately contacted the push crew and asked if everyone was okay; they responded that all personnel and equipment was fine. I then contacted the flight attendants and asked if they were okay; our number 1 informed me that he may have injured his back. After contacting Operations I asked for the aircraft to be towed to the gate. I made an entry in the logbook and asked Maintenance to inspect the aircraft for damage. I then contacted the union for guidance; the Dispatch duty manager and met with a flight attendant manager. We were later given the all clear from Maintenance; the number 1 was replaced and we continued to ZZZ1.Cause: We began our day in ZZZ2; after being picked up a few minutes late by our driver we encountered a multiple car collision on the highway. I contacted our Dispatcher and he informed us that he would pass the information on to ZZZ2 Operations. 45 minutes later we got to the gate just before departure time. Now we are running late and several weather deviations and re-routes later we get to ZZZ where we change aircraft. Our outbound aircraft was delayed and during boarding I was asked to comfort a teenager who was on her very first flight and was fearful of flying. I gave her a tour of the flight deck and did my best to assure her that this was the safest way to ZZZ1. We then met our two jump seaters and many interruptions later began our pre-flight checks. As I commenced my flows we noticed that fueling was still in progress so I asked the number 1 not to close the boarding door. My FO; later informed me that we had our required fuel and from his vantage point the fueler was nowhere insight. I then asked our jump seaters to exit the flight deck while I proceeded down the jetway to see why we had the refueling memo. After having the Fueler secure the fuel door; I was back in the cockpit drenched in sweat. Suggestions: Just taking hold of the entire situation; slowing down; giving myself more time to complete tasks; using SOPs; My FO is new to the Airline and equipment; although he was extremely helpful and competent.