Confusion regarding the Q point of a transistor
As we know the signal is supposed to apply at the base of the transistor,

This is true for a common emitter or common collector stage, but for a common base stage, the signal will be applied at the emitter.

&quot;with no input signal applied&quot; means the base voltage is zero at some point,

This is not correct. &quot;No signal&quot; in this context means there are no variations about the Q point, or that the AC component of the input voltage is zero. It doesn't mean the instantaneous voltage is zero.

but that means the transistor is off at that point and as a consequence, there will not any collector current, missing something?

It doesn't. The collector current will be whatever is established by the DC bias at the Q point.