No...Your cabinet is not tall enough. That is a nice system, but, the picture you see is 3 feet tall, just about...and that would be about 3-4 weeks into veg for MJ...Oh, and you would want the red bulb for flowering, not blue, which is for veg...Best to have both.

here is some good advice...you evidently don't have experience, so LST or other efforts to make your plant fit that small space would be tedious at best!

figure out what system you want, then design a cabinet/closet to fulfill your needs. peace