Newton's First Law only holds up in a vacuum. If we assume that space is a vacuum and that everything in the Universe is subject to that law, then Newton's Law  does explain the expansion of the Universe, it has been expanding since the big bang because there is nothing to stop it. But if that is the case then dark matter particles have no gravity, if they did the expansion would gradually stop and the Universe would collapse in on itself. Unless of course the Universe has a boundary and is expanding into nothing which would mean there is no matter of any description ahead of the expansion to hold it up.

As has already been said, more questions than answers and every possible answer throws up more questions. And none of them throw any light on what started it all off.