Suggestion:
Objectivism also accepts that "only the physical laws contributed to our existence", and Objectivism is as far from nihilism as possible. So you are not faced with nihilism unless you choose to be.
Objectivism, "in essence, is the concept of man as a heroic being, with his own happiness as the moral purpose of his life, with productive achievement as his noblest activity, and reason as his only absolute." http://aynrandlexicon.com/
Nothing leads "necessarily" from what you say about our existence. It it what you think about our existence now that it exists, that counts. It is the here-and-now, not the "why does life exist" question. At least it isn't that question as far as the "what purpose does the universe have for us" because it has no purpose for us, or for any life. It doesn't know about us, because it doesn't "know" anything.
We have to find our own purpose, and you can choose nihilism in self-pity, or you can pick up your ego from "the dirt and filth of the world, nailed and rivetted to the worst and deadest part of the universe, in the lowest story of the house, the most remote from the heavenly arch…"[1]—then dust it off and pin it on your sleeve and accept "the concept of man as a heroic being, with his own happiness as the moral purpose of his life.."
[1]An Apology of Raymond Sebond", in The Works of Michel de Montaigne, 1865 http://www.animal-rights-library.com/texts-c/montaigne01.htm
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