No:)
The WW1 didn't use to be called this until the second war: until then it was mostly known as the "Great War" or World War - people homed there would not be another War so no need for giving them numbers.
However, the first usage of the WW1 happened already in 1914, by German Ernst Haeckel. It was however not standard usage, and was not really known as a name, but rather an adjective; this was was the first.
The standard usage of WW1 (and WW2) started in 1939, when another World War has started.