I'll relate what I was taught many decades ago, when
BJTs were mainstream and MOSFETs a laughable curiosity.
Assume charge neutrality, and injection of minority carriers
into the base (base current). Each carrier has a minority
carrier lifetime.
Across the base is assumed a sufficiently large potential
(C-E) that it can be neglected (forward active) with regard
to saturation. Now the base wants charge balance on all
the base current carriers busily entering and recombining.
At the collector, carriers may enter when the base is not
neutral (junction blocking depends on this). They contribute
a "fractional neutralization" of charge for as long as they
remain in the base region, the base transit time. Then
another will have to pick up the job.
beta equals storage time divided by transit time, this holds
up pretty well in measurement. Also accounts for Early
voltage, as narrowing base w/ Vcb goes to effective base
width goes to transit time.