Q:

Can you change an iPhone startup screen background from white to black? 

It seems light-coloured iPhones have a white startup background colour with black Apple logo.  As you can’t control the brightness on startup - this screen is offensively bright at night - searing your darkness-adjusted eyes and waking any nearby creature who happens to be peacefully sleeping.  
Can you invert it like on dark-coloured iPhones?  Black background, white Apple logo? 

A:

Unless you jailbreak the phone, no...can't be done.  
The startup screen even ignores the accessibility settings.