6 days is a really tight time frame if this is your first arcade cabinet (took me months using spare hours) but with good planning ahead and not dwelling to much on tiny details it could be possible (but still I think the time'll fly by before you know it). I think you could save a lot of time if you can find a precut (mdf) parts kit or if you already have a design let it CNC cut somewhere. Ofcourse an old existing cabinet is also an option, just make sure to be well informed on it's condition and calculate the time you'll need to gut it, restore it (sanding, filling holes and stuff like that). Also keep in mind the time you'll need for adding several good layers of paint on the MDF (or else one spilled drink will ruin your cabinet) or if you're going to use another material to cover the cabinet. Think about stickers you want to have printed for the sides/control panel/marquee, how many buttons, lay-out, the screen you're using and how you'll attach it in the construction (also will you cover it with a glass plate/acrylic glass or keep it bare and so on).
I wish you the best of luck!