After examining the bolt on the rifle it appears to be a later war production Bolt, due to the roughness of some of the tooling marks. It does lock up very tight though, with no play or movement at all once the bolthandle is turned down. Actually found some of the German proof stamps in the butt stock and according to the serial number even the stock and the handguard matches the barreled receiver
Does the bolt have a Waffenamt stamp? That would tell you who made it. Oberndorf Mausers used WaA63 (1935-39), WaA655 (1938-41), and WaA135 (1941-45) on parts (earlier prewar had different numbers as well). Overlap on years due to the binning system is to be expected on different parts as batches of parts were made and binned until needed. Depending on the factory, bins might have refills of newer Waffenamts ids on top of older ones. A similar situation exists on M-1 Carbines for example.
Given the 1939 date on your receiver and the length of the war, if the bolt is unnumbered, it is also possible that a unnumbered replacement bolt was fitted by an armorer sometime during WWII. It could have occurred during the German surrender where sometimes bolts were put in a separate pile from the rifles. Sometimes bolts were even fitted back in the States by individuals or gunsmiths as k98 bringbacks and parts were common in those days.
The tight lockup unfortunately does not tell you whether or not the rifle has excessive headspace as that is the distance between the bolt face (not the bolt locking lugs) and the datum point in the barrel chamber. The tight lockup relates to the fit of the bolt to the locking lug recesses, which may or may not, tell you that the bolt face distance to the shoulder datum pt. has headspace within specification. If your bolt face is slightly deeper than std and the barrel's chamber is slightly longer than std., then excess headspace from tolerance stacking/wear can exist (with a replacement bolt it can be shorter than spec which is also bad).
This is why you should really have 5.56/.223 headspace gage sets for AR builds--it is uncommon but tolerance stacking even on new parts can leave you with too short headspace (very bad potentially) or too long (also not that good in a semi auto). This is especially true if you are mixing and matching barrels and bolts. That is why go gages and no go gages exist is to warn users when the headspace is beyond specification set by either SAAMI and/or CIP.
Field gages indicate the supposed near maximum length where headspace becomes dangerous due to risks of cartridge separations causing hot gas to enter the receiver which can cause exciting events to occur for the user.
As the 8x57 is a rimless case, the rear of the cartridge is unsupported which is where a lot of the fuss about headspace comes it. Rimmed cases use the rifle's barrel chamber case rim recess to bolt face relationship to determine whether or not in headspace. The difference is that a greater portion of the cartridge is supported by a rimmed chamber than a rimless design cartridge.
A variant of this was the infamous Glock bulge in their .40 caliber barrels a few years ago where the brass bulged where the cartridge was not substantially supported by the barrel chamber.
Depending on the degree of being out of specified go-no go headspace range, it can be worked around to some extent which is beyond a simple post because it depends on the rifle's design, it depends on the shooter's willingness to take risks, whether or not new brass is used, the cartridge design itself, strength and age of the action, accuracy expectations, risk to damaging the rifle (if not the shooter), and so on.
Sorry to run long but these posts are sometimes picked up by Google searches and the like so others might read it years from now.