"Into the Darkness", a novelette by Ross Rocklynne, also the answer to this old question; first published in Astonishing Stories, June 1940, available at the Internet Archive. Does any of these covers ring a bell? As far as the ISFDB knows, the earliest reprint you could have read was in the 1969 paperback anthology Futures Unlimited edited by Alden Norton.
"Into the Darkness" was the first story in Rocklynne's Darkness series, which was collected under the title The Sun Destroyers as half of an Ace Double Novel. The other stories in the series are also available at the Internet Archive: "Daughter of Darkness", "Abyss of Darkness", and "Rebel of the Darkness" aka "Revolt of the Devil Star".
The main character (called Darkness) of "Into the Darkness" is not a star system but an immense space-dwelling energy being:
Out in space, on the lip of the farthest galaxy, and betwixt two star clusters, there came into being a luminiferous globe that radiated for light-years around. A life had been born!
It became aware of light; one of its visions had become activated. First it saw the innumerable suns and nebulae whose radiated energy now fed it. Beyond that it saw a dense, impenetrable darkness.
The darkness intrigued it. It could understand the stars, but the darkness it could not. The babe probed outward several light-years and met only lightlessness. It probed further, and further, but there was no light. Only after its visions could not delve deeper did it give up, but a strange seed had been sown; that there was light on the far edge of the darkness became its innate conviction.
Wonders never seemed to cease parading themselves before this newly born. It became aware of another personality hovering near, an energy creature thirty millions of miles across. At its core hung a globe of subtly glowing green light one million miles in diameter.
He explored this being with his vision, and it remained still during his inspection. He felt strange forces plucking at him, forces that filled him to overflowing with peacefulness. At once, he discovered a system of energy waves having marvelous possibilities.
"Who are you?" these waves were able to inquire of that other life.
Softly soothing, he received answer.
"I am your mother."
"You are my son—my creation. I shall call you—Darkness. Lie here and grow, Darkness, and when you are many times larger, I will come again."
At story's end Darkness makes a planet, possibly ours:
He concentrated on the sudden thought that struck him. He was dying, of that he was well aware, but he was dying without doing anything. What had he actually done, in this life of his?
"But what can I do? I am alone," he thought vaguely. Then, "I could make a planet, and I could put the life germ on it. Oldster taught me that."
Suddenly he has afraid he would die before he created this planet. He set his mind to it, and began to strip from the sphere of tight matter vast quantities of energy, then condensed it to form matter more attenuated. With lagging power, he formed mass after mass of matter, ranging all through the ninety-eight elements that he knew.
Fifty thousand years saw the planet's first stage of completion. It had become a tiny sphere some fifteen thousand miles in diameter. With a heat ray he then boiled it, and with another ray cooled its crust, at the same time forming oceans and continents on its surface. Both water and land, he knew, were necessary to life which was bound by nature of its construction to the surface of a planet.
Then came the final, completing touch. No other being had ever deliberately done what Darkness did then. Carefully, he created an infinitesimal splash of life-perpetuating protoplasm; he dropped it aimlessly into a tiny wrinkle on the planet's surface.
He looked at the finished work, the most perfect planet he or his playmates had ever created, with satisfaction, notwithstanding the dull pain of weariness that throbbed through the complex energy fields of his body.
Then he took the planet up in a tractor ray, and swung it around and around, as he now so vividly recalled doing in his childhood. He gave it a swift angular velocity, and then shot it off at a tangent, in a direction along the line of which he was reasonably sure lay his own universe. He watched it with dulling visions. It receded into the darkness that would surround it for ages, and then it was a pinpoint, and then nothing.
"It is gone," he said, somehow wretchedly lonely because of that, "but it will reach the universe; perhaps for millions of years it will traverse the galaxies unmolested. Then a sun will reach out and claim it. There will be life upon it, life that will grow until it is intelligent, and will say it has a soul, and purpose in existing."