That last sentence is completely incorrect and is enough for me to safely disregard everything else you just said on the basis you don’t actually know what you’re talking about.
It’s easy to prove me wrong: point me to the relevant lines in the relevant treaties or conventions that state this.
You can’t because they don’t exist. There is no obligation to seek asylum in the “first safe country.” This is a common trope trotted out by right-wing mouthpieces which is where I’m assuming you got the rest of your “facts.”