I would say 20's to 50's. From my area the early ones all have a pedestal or foot on the base, which phased out in the late teens to early 20's, replaced with the style shown.
Interesting, it looks like Brooklawn either stole the bottle from an existing firm in Chicago, or maybe that firm went out of business, and they re-etched it. I have a Brooklawn Club ACL soda bottle from Bridgeport, CT that dates to the 1940s.