One course of action might be to write to them saying you intend to use the space and willlodge a monthly amount to an account in earnest of your good faith to show that you intend to pay for the space and inform them of your action.
Say you are only doing this to have a foot in the door and not to acquire legal rights - if they own it and they know it, you'll find out pretty quickly.
The payments mentioned above do not constitute evidence of holding a lease in the absence of formal signed documentation, merely that you are sincere and not trying to squat.
Actually using the space without a lease is a form of traspass I think, so you may be on very shaky ground here, but informing them and paying the money to the account shows you had no malicious intent on your part.
This is why I think the best course here would be to state your intention, but not actually act and wait for a reply.
As in all things advised on AAM, get professional advice before you act in RL.
ONQ.