The Cosmological Argument is one of the most popular arguments for the existence of God, and a cornerstone of debate between Atheists and Theists.
It is an old argument, and has been defended by countless theologians from multiple faiths over the centuries. It has various formulations, and many brilliant people have brilliantly defended it against proposed objections from Atheists.
Ultimately, regardless of the particulars of the arguments given from either side, at base, there are only two hypotheses being proposed:
Attempts to justify clinging to #2 are not worthy of serious consideration. It is intuitive that the constituent elements of this universe - matter-energy, natural laws, and so on - are the products of intelligence. These things are deaf, and dumb, yet they have properties - mass, charge, behavior, etc. - which demand an explanation. Their bare existence demands an explanation. Also, their continuing to exist demands an explanation.
And, there is no possible explanation for why all of these things exist, and have the properties that they have, other than that they are contingent creations of an intelligent God, who created them, gave them all their properties, and sustains them. There are no other answers which are even possible, as any other alternatives terminate in there being no intellect at the base of this reality, which fails to answer the "why" question that all of creation, with its mere existence, demands to be answered:
Leonard Susskind - The Cosmic Landscape, Introduction
The Laws of Physics begin with a list of elementary particles like electrons, quarks, and photons, each with special properties such as mass and electric charge. These are the objects that everything else is built out of. No one knows why the list is what it is or why the properties of these particles are exactly what they are. An infinite number of other lists is equally possible. But a universe filled with life is by no means a generic expectation. Eliminating any of these particles (electrons, quarks, or photons), or even changing their properties a modest amount, would cause conventional chemistry to collapse. This is obviously so for the electrons and for the quarks that make up protons and neutrons. Without these there could be no atoms at all.
Imagine that all of reality consisted of a single hydrogen atom suspended in an otherwise empty void. The same questions would remain - why does it exist? Why does it possess mass, charge, structure, and predictable behavior? It is intuitive that such an object, possessing properties that it did not give itself, is the product of intelligence. Multiplying the number of particles until the problem is universe-sized changes nothing about that fact.
Both the Materialist hypothesis and the Theological hypothesis have a "brute fact" of existence at their root - the universe, and God, respectively. But, they answer different questions. The Materialist hypothesis actually leaves every question on materialistic origins unanswered, by stating that the system has always existed, for absolutely no reason. The Theological hypothesis actually proposes an answer to materialistic origins - an intelligent mind, which has agency, and chose to make the universe as it is. One is grounded in total arbitrariness and incomprehensibility, the other is grounded in intentionality and intellect. Not all "brute facts" are created equal.
Why is there something rather than nothing? Because an uncaused God, who is supremely intelligent and powerful, made it. There is no other explanation for why things exist, and have the properties that they have.
The Cosmological Argument, by itself, is enough. It is a sound argument, and in my opinion, it is best taken simply and intuitively. If you are one who struggles with faith, or find yourself perpetually returning to this problem, I would exhort you to allow yourself to let it be enough, and move on to bigger and more interesting questions in life.