Can a transistor transistion between cut-off and active without going through the linear region?
Here is the measurement simulation of a real fake transistor:


As you can see in the behaviour of VBE and VCE, the transistor indeed goes through the linear region while switching.

A transistor cannot switch with infinite speed.
The base (and other parts) actually have a small capacitance, so it must be (dis)charged similar to a capacitor, which takes time.