One of the most common mistakes made by a lot of folks here is to treat transistors as a fixed and unique ingredient. Their reasoning is that you could not substitute marjoram for sugar or habaneros in a recipe, simply by adjusting the balance of other ingredients. So if it SAYS to use such-and-such a transistor, then that's what you have to use.
The truth is somewhere within commuting distance from that, but not exactly that.
The goal is to provide enough gain to a signal that it runs into serious headroom issues that result in a flattening of the peaks of the signal. But that running-out-of-headroom can be achieved in many ways. It is certainly helped by greater gain, but does not depend exclusively on it. The requisite gain, and risk of insufficient headrom, can be achieved in many ways, and one of those is via the biasing of the transistor.
In many instances, that biasing is relatively specific to the specs of the specific transistor. The schematic may stipulate the values of the biasing components, but those are really only ballpark figures, in anticipation of roughly what a given transistor number might require. When it comes to op-amps, the gain you get IS a clear and unambiguous function of the gain-setting resistors. But then, op-amps are more complex beasts, internally, and designed so as to render moot any characteristics or idiosyncracies of the op-amp. Transistors are simpler devices, with their own idiosyncracies, such that the gain you get could be a little higher or lower than what the stated biasing component values might suggest, all because of the specs of THAT transistor unit.
But the corollary to all of this is that a great many different transistors could be used to achieve the exact same end. If we were all equally capable of calculating the required biasing components, all a schematic would need to say is "NPN transistor here" and the required gain and offset (i.e., precisely centered in the middle of the voltage swing, or asymmetrically situated) for that stage. But sadly, most of us are not so skilled (myself included), leaving us to rely - perhaps a little too much - on the stated biasing component values, and the suggested transistor numbers.
HOWEVER... it is not wrong to ask the experts here what one would tweak in order to get transistor X, with such-and-such specs, to perform in the desired way.
