You might have an OEM unit. Many Terex machines are rebranded. For example, some older Terex compact excavators were actually built by Yanmar or Kobelco. If the dealer cannot find it, ask them to run a "cross-reference search" or call Terex corporate archives directly (for antique or vintage equipment).
The serial number is typically engraved on a thin metal ID plate (often about the size of a business card). Common locations include: terex serial number lookup
The Ultimate Guide to Terex Serial Number Lookup: Find Parts, Manuals, and Machine Specs You might have an OEM unit
The serial number is typically found on a metal ID plate (data plate) located in specific areas based on the machine type: terex serial number lookup
Digits indicating the exact production year or production sequence. Unique Identifier