No disrespect intended, but you're making this whole thing sound way more challenging than it actually is, almost like it's something out of a Mission Impossible movie. 😂Perfect 👏. Use a led light or a full white screen and look for particles. Very unlikely its clean.
You need a clean room for installing it without getting contanimation from the atmosphere, plus the silicone film of the protector must be absolutely clean.
I've installed many screen protectors for my family and it probably went well 98% of times.
Once you inspect the screen for the final time and you're sure that it's 100% clean, you have to lay down the protector immediately and in that split second it's unlikely to get particles stuck between the glass and the screen, unless you're really really unlucky or you're applying it on a dusty surface.