What if the trespassers just ignore the sign, and walk on/over the privately owned land without the landowner ever becoming aware of it? How could the landowner sue the unknown trespassers when there wasn't even any evidence of their trespassing?

What about a security camera?

What about a security camera? What can the landowner do if they've already left the private land without committing any crimes?

Yes, that's what I was asking. Your previous comment indicated the homeowner needed evidence in order to sue for trespassing. But it seems there was no crime committed after all.