Everyone I know, including myself, wants a sandbox mode. However consider the problem with your statement of "live pvp".
Right now for everything I have seen that is "live", like TW or GAC, whenever someone battles, it shows that the opponent is currently attacking that squad, but it gives a delay when the opponent finishes the battle, like around a few seconds. This can make the sandbox mode irritating especially if a time limit is set on those battles, as there will be a significant delay: the opponent will take time to think which ability to use, who to target, etc etc, plus that loading delay.
I would suggest that rather than your ally playing live, we could have an option to select an ally's roster, choose units or datacrons for an 'opponent' squad, and let the AI battle from it, so the delay isn't there and, besides, as sandbox is for practise, going against the AI makes sense since every battle that exists is against the AI, so I agree with your second suggestion on sandbox
Other than that, WE NEED SANDBOX!!! It could be 'managed' by that Kel Dor NPC (like as a tutorial when a player opens it for the first time), who sits near the challenges too, as he also says "I've been dusting off my old military texts to come up with new Challenges for you" when he is clicked