It's definitely a Cosmos as I did some further checking and the name of the company was known as Cosmos B. Schild & Co. The legible letters on the headbadge decal are B.SC..... which I guess proves it. I found a picture of a 1938 Cosmos and the head badge isn't very clear, but I could pick out the image of the world with a winged wheel on top. The pedals on this bike were the same as yours by the way.
I did find a picture of an old enamel head badge with the world with winged wheel on top image, but the wording on the badge was 'BIEL' which had me confused until I discovered that Biel is the name of the Swiss town where the Cosmos factory is.
I also found a picture of a chap in a bicycle shop repairing an old Cosmos bicycle and the mudguards were the same as the ones on your bike.
Sooooo I think we can put the case to rest; - it's a prewar Cosmos