Yeah it can be tough to be greeted by this ‘flashbang’ when trying to read something late at night.
If you’re using dark mode, the app starts with a white background before transitioning to black. I believe that’s what the OP means by “white flash”.
I have it installed as a home screen app. There's no white flash in Safari, but a flash does occur when you launch the installed app.
Unfortunately, a white background is the default for webpages in most (all?) browser user-agent style sheets, so while the PWA loads its own styles (which will override the white with black) you will see white. This may last for more or less time depending on if the PWA is cached, how its assets are handled by its service worker, how fast your network is, how fast your phone is, etc, but it’s not something that can be “fixed” in all cases by the app/site developer - you’ll need the browser vendor to address it (don’t hold your breath).