The smallest file-size would be to do Image.import(...) in App::Init(), if you don't mind a bit of loading? That way you can get the predictive qualities of png compression, yet still keep it fast in memory. Else, another lossless reduction would be the release .pak compression on the 350mb file. I'm not an expert in this area though.
Importing images is described in the textbook "EsenthelEngineSDK\Tutorials\Source\Advanced\1 - Geometry, Graphics, Gui, Misc, Net, Sound\Graphics\Import Image.cpp"
Here is my example:
It is the whole texture, in the resolution of 6144x1024px(6 images in 1024x1024) and size - 1.78mb
Also, if you want to understand how to position the image in the skybox texture - see "EsenthelEngineSDK \ Data \ Gfx \ Sky \ skybox.jpg"