Proving theft in this case should all come down to what the company previously communicated in writing to employees about making such purchases. Was there a policy about buying spirit wear? It should have covered who was permitted to order the apparel, when, whether employees could do so for personal use, how to reimburse the organization, what authorization was required, etc. Also important is the electronic access to the system. Did you and your co-workers have authorized access to make the order or did you use someone else’s log-on?
There are other policies that are also potentially relevant here. Your organization should hopefully have a policy regarding discipline, theft, and employee investigations. If this was a genuine misunderstanding and there was no written communication prohibiting it, push back on any discipline. Be ready to explain, however, how you had planned to reimburse the organization for the expense of the spirit wear.