The engines are also very far from the cockpit, and behind them. They hear them, but not well.
So it’s not that surprising they didn’t immediately notice the problem.
That they did notice, and relatively quickly, is a sign of how well they did. But seconds matter in this scenario, and by then the lag to spin up resulted in no significant change of thrust before impact.
If a pilot doesn't pay attention to where his thrust levers are when appropriate thrust is critical to safe flight, that is pilot error.
A go-around isn't complicated enough to merit reliance on automation anyway: Max thrust (or whatever is appropriate), pitch up and climb according to ATC orders or go-around procedure at airport, landing gears up, and come back for another landing attempt.
In this scenario, the auto throttle doesn’t auto throttle up because unexpectedly, they were partially wheels down for a moment, and that disables auto throttle up.
Oops.
Definitely one of those ‘if the PIC had been a little more paranoid, and a bunch of other rare/weird things had not happened, it would have been fine’ type accidents. The first officer was supposed to also verify things, but the specific step wasn’t in the training either, and wasn’t normally applicable because of the TO/GA automation.
Luckily no loss of life from the crash directly. If the firefighters had listened to prior crash issues and fixed them in their own response, likely no firefighters would have died either.
On multi-engine jets, common training is to remove your hand from the throttle at V1 (takeoff decision speed). Most problems after that speed are to be taken airborne and dealt with there.
(In fact, this idea of gravity-relative-to-butt is very strong in people and when that fails to be a useful model is often when we see accidents happen.)
It's the same in a car, if you are coasting in neutral and encounter a hill, even though the car will be slowing down there is no "perceptible" longitudinal acceleration because it's caused by gravity (equally acting on the car and the occupant), just like in space or one of those zero-G flights.
There would be an increase in drag when pitching up, that would also cause deceleration.