>>534897372 days, meaning a 48 hour cooldown from the last time the box was activated.
Niantic is piss poor at communicating when you can recharge the box (and many other things), the countdown re-calculates when the app is launched, so it can say 1 day remaining when it might actually be ready to be recharged.
The Let's Go event runs from Tuesday, March 21, at 10:00 AM until Wednesday, March 29, at 8:00 PM Local Time.
If you want to maximise your mystery box usage, activate your first box no later than 7pm on Tuesday, and then you can repeat activation on Thursday 23rd, Saturday 25th, Monday 27th, and Wednesday 29th.