Question: I'm installing a NEMA 6-50 outlet in a garage for future potential car charging. The wire is a #6 3-wire, red, black, and white.

I'm not used to this size wire, and it's very stiff and hard to fit into the box. The box is a metal 4x4 inch box, but it still seems difficult to get the wire in the box once it's screwed into the outlet. The wire extends maybe 3 or 4 inches into the box.

So my questions are:

Is my box big enough, or do I just need to cut the wires shorter? Ideally I'd want a longer box to more easily accommodate these thick wires. I'm guessing the box is large enough, since I can't seem to find anything bigger. I'm more used to cutting the wires long enough that I can make them extend out the box a bit, and then push them out, but 6 gauge is so stiff, this is difficult. I've not wanted to cut the wires too short for obvious reasons.

Can I pigtail the ground wire with a smaller wire, and connect that smaller wire to the outlet, or does the ground wire have to be 6 gauge? This was one idea I had to make getting these wires to more easily fit the outlet, but I don't know if it's legal/safe.

Answer: 
You can't use that cable for a new outlet. It needs to go to the scrapper.

You'll need to re-run it with proper wire or cable, such as 6/2 **w/ ground**.

Given your complaints about the stiffness of #6 wire, I'd suggest running some sort of conduit, such as "smurf tube", and run individual THHN wires in the conduit. That would do a couple of things for you. First, you'd be able to use #8 stranded wire for 50A, since THHN is allowed a higher operating temperature. Second, you could defer the "neutral" question and simply add the neutral wire later if needed.
I think all irrelevant due to what I see as an illegal install from day one, but when replacing with legal cable the NEC requirement is minimum 6" of free conductor from where it emerges from sheath.

The NEC has box fill limits, 5 in³ for #6, 3 in³ for #10 (ground up to 60A), adding 2 wire count for each yoke used (or 4 wire count if device wider than 2"). So (3x5)+3+(2x5)= 28 in³ minimum box size required.

Adding splices rated for higher temperature wire is not going to make it easier.

I don't see how your wire was ever a legal install, and don't see any provision that code allows running a ground separate from inside a cable as a legal install. The code has provision to add a ground when replacing an ungrounded receptacle with a grounded receptacle, but if you can't establish that this was a special 250.140 exception circuit that allowed grounding ranges and dryers via the white neutral conductor then you never had a legal install to begin with. You might get a local inspector to grant you latitude beyond code, but I wouldn't count on it.