The serial number on the Bambu Lab machine will be printed on a small sticker with the serial number and serial number QR-Code. This QR-Code can also be read by most smartphones when taking a photo. The placement of this sticker is explained below:
Bambu Labs P1 Series and X1 Series have the serial number sticker situated inside the machine on the upper right side corner.
Bambu Labs A1 Series have the serial number sticker situated visibly on the rear exterior of the machine.
Bambu Labs H2D has the serial number situated inside on the right panel corner.
The Original AMS has the serial number sticker situated inside on one of the dividing walls.
For more Serial Number info from Bambu Labs: https://wiki.bambulab.com/en/general/find-sn