You might look on the outside of the right front frame rail, near a shackle, truck SN might be stamped there. Stamped # on right side of engine on a machined pad, just behind the distributor, engine SN starts w/ displacement, i.e., 270xxxx.

Nice truck

'37 GMC T-18 w/ DD 4-53T, RTO-610, 6231 aux., '95 GMC running gear, full disc brakes, power steering, 22.5 wheels and tires.
'47 GMC 1 ton w/ 302, NP-540, 4wd, full width Blazer front axle.
'54 GMC 630 w/ 503 gasser, 5 speed, ex fire truck, shortened WB 4', install 8' bed.
'55 GMC 370 w/270, 420 4 speed, grain, dump bed truck from ND. Works OK.