I've worked extensively with brushed DC motors.
The startup current is only limited by the armature resistance, which on a motor this size will be between 1 and 2 ohm.
Therefore all brushed DC motors must be soft started, either by a reduced voltage or a tapped resistor whose taps are sequentially shorted out.
I would assume that since this is a DC to DC conversion, the startup could be achieved by a current limit feedback.
Something that the OP poster has not told us is what type of DC motor it is. Is it Permanent magnet or does it have a separate field connection? If the latter, then a constant voltage field supply will be required.