I speculate, however, that the grain would have been almost immediately engulfed. To illustrate this, consider a chamber pressure of 1.0 Mpa. This is equivalent to about 10 atmospheres pressure. This means that the original volume of "cold" air in the motor would have been reduced to 1/10th its original volume, with the remaining 9/10th the motor volume being filled with hot combustion gases. Under this condition, it would seem probable that combustion would occur on all surfaces exposed to this influx. And this order of pressure was reached very quickly after ignition.
The more likely reason for the delayed pressure build-up was a combination of an insufficiently effective pyrotechnic igniter*, combined with an unusually large chamber duct (free) volume due to the rectangular grain geometry. With the igniter failing to generate significant pressure within the motor (perhaps by not burning quickly enough), the propellant burn rate would have been initially minimal. Thus generation of combustion gases and resulting pressure build-up would have been delayed, as indicated on the pressure-time curves. Note that an initial pressure spike, which can be attributed to the igniter charge, is not seen on any of the curves.
This scenario of delayed pressure build-up is, in fact, similar to what I had experienced with my rocket motors prior to my using pyrotechnic igniters.
*The igniter consisted on a blackpowder-filled cardboard tube, 16mm (0.63 in.) diameter by 35mm (1.38 in.) in length.