U can get to -20 if u insulate it properly. A modern TEC would give u a 50 degree C differential using optimum conditions and optimum currents with optimum cooling.
U will need a sizable heatsink and cooling fan, or perhaps a PC water cooling rig to ensure the -30 deg C. Only possible if TEC hot side is kept under 20deg C, otherwise u will have to stack TECs which is more complicated.
However, does your SSD generate any wattage load?
It seems u want -30 deg C or better. This won't require any 'control' just insulation, heatsinking & a continuous regulated powersupply....at near the 15VDC rated of the TEC.
here's a nice logic level beefy FET for u:
VISHAY SILICONIX
IRLZ44PBF
Should run 5A without needing a big heatsink