What is the minimum time span to trade a future contract?

It depends on what you mean by trading the futures contract.

If you're a speculator who bought the thing in hopes of selling it for a profit before the settlement date (this happens all the time, and my opinion is it's stupid to do so--you're more likely to lose money speculating on futures than you are in making it) the minimum time is the time it takes for the price of the underlying commodity to go up enough that you'll make money on the deal.

If you use the underlying commodity...well, let's just say you could buy a futures contract from one of the idiots in the last paragraph the day before the settlement date.