To be fair, somewhere in the middle of it, you mentioned you had put an invisible statue in a room and gave your PCs zero chance of detecting its presence. To which, I came in asking why there couldn't be even a tiny chance, based on faint, yet possible, environmental factors. Followed by you going a little off the rails demanding I provide proof a Hide action is required to go unnoticed (which had nothing to do with my post, nor my POV on the subject)...
If you walk into a room (and don't walk into the thing) I think it would be virtually impossible to detect an invisible statue unless you interact with it somehow in many (not all) cases. It would be no different than if I blindfolded you, took you into a room you had never been in and asked you to describe where all the furniture was. Unless you're DareDevil it's not going to happen.
A clean spot on the floor of a dust covered room? All you would know was that there is a weird clean spot on the floor. A weird indentation in the dirt? Could be just a weird indentation. If you notice something like that (which I'd base on passive perception) it's the start of an investigation encounter that could be resolved in any number of ways.
You might be able to detect it if snow is blowing in through an open window, or a ray of light shining down illuminating dust particles except where the statue is.
You would definitely know something was there if there's a pigeon sitting on it. Or vines have grown up around part of it. Or the room is half flooded except for a statue sized hole. Or
some indication that there's an invisible object there.
There are situations where the DM has to set a DC. If that DC is so high it is unobtainable then there's no need for rolling. For my invisible statue scenario, what that DC is will be based on too many environmental factors to list.
Walk around the room, do some investigation, throw some flour around because you suspect there's something there and it's a different story.
There's nothing wrong with letting people know it's there, it's just not something covered by the rules IMHO. As a DM I wouldn't do something like this to be a "gotcha" but as a fun investigation encounter/high level trap/surprise dedication ceremony? Sure.