FAR 25:
Sec. 25.119 Landing climb: All-engine-operating.
In the landing configuration, the steady gradient of climb may not be less than 3.2 percent, with--
(a) The engines at the power or thrust that is available eight seconds after initiation of movement of the power or thrust controls from the minimum flight idle to the go-around power or thrust setting; and
(b) A climb speed of not more than 1.3 VS.
[Doc. No. 5066, 29 FR 18291, Dec. 24, 1964, as amended by Amdt. 25-84, 60 FR 30749, June 9, 1995]
As a consequence of that, credit cannot be taken for any thrust level above that achieved after 8 seconds. It is therefore a well balanced design if flight idle is set such that TOGA is achieved within the 8 second window. Since the rule specifies the minimum thrust, where the pilot actually has the throttle doesn't matter.
From this rule you could deduce that all engines likely have spool-up times from idle to max power of approximately 7 seconds, for the go-around case.