The 7x57 is not the first smokeless military round. It came out in 1892 and was used with deadly effect by Spanish troops in Cuba, and by Boer Commandos in South Africa in models 1893 and 1895 Mausers.

I do believe that the 7x57 and the 1895 .30WCF, aka the 30-30, are the worlds first widespread smokeless sporting cartridges. The 7x57 caught on quickly in Europe, Africa, and throughout the British Empire.