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How do I establish a network printer connection for multiple Active Directory users without having them sign onto their account first?
While probably not the answer you are looking for, you don't. Authenticating users prior to granting them access to resources is a cornerstone concept in Microsoft resource access. One option, though I would recommend against it, would be to configure the printer as a direct print device using "Standard TCP/IP Port" which would allow anyone to print to the printer without using your Windows Active Directory at all.