Use it individually. Texture atlases are used to gain efficiency by minimising texture swaps for many small textures, and avoiding wastage due to textures having to be bumped up in size to dimensions that are a power-of-two. A single image on an atlas gains you nothing except more book-keeping, and if the atlases are required to be power-of-two in size, your example image would need to be 2048x2048. That's a lot of wasted space.
The original tags included Android, which brings some extra factors to the discussion:
A 1920 x 1080 image will most likely need to be compressed to work on Android anyway, which comes with a need for power-of-two sizing. PNG is not a native format, so any PNG images will have to be converted and probably compressed before use. So even storing and using it individually, for loading and rendering it will be bumped up to 2048x2048 before it's compressed. You could use it at its native resolution uncompressed, but it would be massive in memory, and you probably want to avoid that. In practice we've always used compression on full-screen backdrops, but left texture atlases uncompressed (because the quality drop is far more noticeable on the smaller sprites); that's a pretty common policy for most places I believe.