I don't have a straightforward answer but I narrowed it down to one likely candidate. I believe your piece was made by the Central Glass Works of Wheeling WV. The monogram on the base of the container is "C" and "G". Central Glass operated from 1896 to 1939; according to glassbottlemarks.com, they were known to produce milk glass. I am unable to find a specimen attributed to Central Glass that has the same markings as yours.
Below is a photo by the esteemed Lewise Hine taken in 1908 at the Central Glass Works factory.
Thank you I think that looks like a good match, I have searched through the internet checked the websites you linked and sha.org but can't find any examples of that mongram either. Is their a possibility that it could be foreign?
This is just my opinion, but I strongly doubt the monogram stands for Central Glass Works. The type of milk glass that Central made was mostly pattern glass (tableware), not utilitarian containers.
I suspect (but cannot prove) that the CG monogram is the initials standing for either the brand name of the cold cream or cosmetic product that was sold in the jar, or the initials of the cosmetic company that produced the product. Most of the milkglass jars with that "look" held a cosmetic product such as face cream.