I would be interested to know, what speakers you can get that have a very VERY low current draw when there is no signal being sent to them.
I guess it's a question of how fast can a chip turn on power to an amp that is driving the speakers.
What would help a LOT, and I'm guessing this is not the case, but Amazon could alter this.
Take this scenario. You have the Dot, its sitting waiting for the keyword.
You say Alexa, the blue dial lights up as it's now listening.
At this very moment, the second the blue light goes on, it could send some, even silent(ish) signal to the external speaker to give it that extra few seconds to, as it were fire up, whilst you are speaking, ready for a glitch free audio response from the Dot.
Even if you said "Alexa, what is the time" that's still a generous 2 seconds at least really.
I don't know how it's done, but that could be enough time for a amp to go from standby and a very low power/standby mode into being able to output audio.