I have a slightly different interpretation. When calling someone, they hear "ring" then silence, then it repeats. Unless the person interrupts a ring, the caller won't know it's picked up for a second.
As an aside, I mess with my wife like that. I answer the phone without saying something. There's a long pause, then she says something like "oh, did you pick up?"
So, I say the person being called should speak first. A solid "hello" and maybe even a "this is [name]"
Then the caller can get right to what they want.
I get a lot of random numbers for business, and this method results in less awkward stumbling from both sides.