How wonderful that you have your father's top hat. Judging only by your photos, I might date the hat to around the 1930s to 1940s. Hard for me to say, so this is really just an educate guess on my part. The interior construction is 20th century, the sides and crown are made of silk plush, the brim looks to be a silk faille or other silk material, with silk petersham/grosgrain ribbon for the brim's edge and the hat band.
It looks to be in very good condition. Do you know what size it is? Larger sizes of this style top hat, in good condition, are quite sought after.