Motherboards (like other components and sub-assemblies) will either have a manufacturing date OR a date code. The date code may be a discreet marking or sometimes is integrated into the Serial # - this is purely for traceability, recalls, warranty, etc.
If you do not see a date or a date code, then the manufacturing date is integrated into the Serial #. Place a call to Asus tech support if necessary.
Certain products, like Nikon cameras, for business reasons will not disclose the manufacturing date.