Pull the forend off and take the bbls off the action..
Check for marks on the bbl flats or ahead of the bbl flats on the tubes. Also any marks on the action flats or face of the breach. The latter usually small and centered either up high or low on the breach face are makers marks..
BBl and action flat Marks would include ser#, (foreign) proof marks, inspector marks, proof date codes (depending on the country/mfg) and sometimes letter initials that can indicate the gun maker, bbl tube supplier, ect. With that it's sometimes possible to narrow down the mfg period at least to an era or decade(s) if not the specific yr it was proofed.
Doesn't look like too bad of a shotgun,,steel bbls, decent wood, screws aren't all buggered up, dolls head with underlug lock up. hammer thumbpieces appear to be matching