That’s a nice score!
The bike was made for Sears by H.P. Snyder Manufacturing Company of Little Falls New York (think Rollfast). The fork crown and the arched rear fender bridge are the give-a-ways. The spacer between the rear fender and the bridge is there because the same frame was used for both 28” single tube and 26” balloon tire applications.
It is likely that your bike dates from 1935, Most Elgins from the time were supplied by Westfield Manufacturing (think Columbia) but the 1935 catalog depicts some Snyder made Moto-Balloon bicycles. By 1936 it appears that Sears had returned to sourcing from Westfield
It looks like the bike should clean up nicely and is generally quite complete. The horn, the saddle and the pedals are newer than the bike. The original saddle would have had longer compound cylindrical springs.
Bikeriderx recently posted pictures of a girl’s Snyder from the same period and likely the same year. If you don’t mind posting the serial number it would make an interesting comparison
Phil