As near as I can recall, the engine stampings happen at engine assembly, at the time the engine is actually being assembled. There is info related to the actual assembly process sometimes included in the pad stamping that indicate certain facts, such as undersized turnings and bearings that would not be known until the assembly process is underway. However, the assembly date of the motor can be days before the build date of the car, as there needs to be many assemblies to fill the line with sales bank cars, fleet orders and such. I believe the actual VIN is stamped on the motor when it is mated to the chassis, either from the build sheet or IBM card to correlate the motor to the car it is destined for. As a body came down the line, it was imperative that the chassis be assembled and ready to continue, therefore the motor would already be stamped before it is mounted.
As for the fender tag, it has always been my knowledge that the fender tag is painted with the body, and that the purpose of the fender tag is to call out the "punch list", or what holes need to be punched and what fixtures need to be present for that car. Since it also calls out the paint and trim codes, which is mostly for paint, it was hung by a wire on the car early on the line and attached to the fender at paint.
So, to try to answer your question, could the motor be built one day after the car was assembled?? Of course, if only by way of waiting for a certain part to arrive, or if something held up the motor or chassis for some reason. Damage to bodies happened all the time, and repaints were frequent, so who knows what happened to either assembly. Parts shortages could also suspend a build depending on what the shortage was, so it's entirely possible that the motor could be assembled one day after the build date of the body!!
Thats my story and I'm stickin' to it!!Geof