For the sake of my collection, I count 1,039/Smoothed Out Slappy Hours as the first album released by Green Day. However, this is actually a compilation album including every song from the band's true first album, 39/Smooth, as well as songs from the EPs 1,000 Hours and Slappy. The reason that I count this record as the "first" is that 39/Smooth was only released as a vinyl record, never being officially printed to a CD. This will have to do, as I don't have the equipment (or money) (or time) (or patience) to maintain a vinyl collection.
39/Smooth was the first and only Green Day album to feature John Kiffmeyer as the band's drummer. After this record, he was replaced by Frank Wright, better known by his stage name Tré Cool.