Is mathematics the necessary cause for the universe? Can physical laws or mathematical laws in themselves be the cause of emergence of the universe given that they are always true and absolute in nature?
No, they still require a cause or designer (a "programmer", if you will); otherwise, something is still eternally pre-existing for no reason.
We also can't be certain that, if there were a different universe, all of these things would be the same, even if it seems obvious to us here. (Whether or not they would necessarily be the same is, necessarily, speculative.)
However, it is a good question!