Before getting to the argument, Some important definitions must be presented:

A necessary: a thing that the supposition of whose nonexistence entails an impossibility.
An Impossible: a thing that the supposition of whose existence entails an impossibility.
Contingency/possibility: the negation of necessity i.e. a thing that the supposition of whose existence or non-existence does not entail an impossibility.

A necessary being: a thing that its nature necessitate/guarantees its existence. it exists through itself, not through another. Existence is essential to it. its essence is not susceptible to nothingness, therefore it has always been existent, so it had never been brought to existence. it is neither caused by something nor is dependent on/lacking/needing something. and it cannot be complex i.e., composite of parts. its essence can not change.

An Impossible being: its nature necessitates its non-existence i.e its nature precludes its existence. the supposition of whose existence would entail an impossibility, its non existence is necessary, can not exist. it's not a thing it's pure nothingness.

A contingent being: its nature neither necessitate its existence nor its nonexistence. i.e it's not necessary being nor an impossible. it's possible to exist or not exist, its essence are susceptible to be caused/changed/affected. it does not exist through itself but through another.

and the jew philosopher, Ibn Kammuna recapitulates all these points by saying "Necessity, possibility and impossibility are self-evident concepts. everyone knows that a man must be an animal, might be a writer and is impossible to be a stone."

Substance: What does not exist in another and not said of another.
Accidents: What exists in and is said of another.

Causing by nature/necessity: to causing by obligation. For instance, the fire burns by nature/necessity, meaning that the fire does not choose to burn or not, it's intrinsic/substantial to the fire to burn. so what is causing by nature is causing by necessity. and the effect would

NOTE: i'm gonna use the word CREATED as something that has a beginning of its existence, that specific meaning. not more, not less.
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A) the existence of a necessary cause

1- Whatever is contingent must have a cause
2- the universe is contingent
3- therefore the universe must have a cause
4- an actual infinite regress cannot exist
5- therefore the cause must be necessary

Premise 1 is self-evident, it doesn't need to be proven. it's known as soon as the definition of the term is known.
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Premise 2, states that the universe is contingent, and we can prove it in many ways:

the first is conceptual; it's not impossible nor does it entail an impossibility to say that the universe could not have existed or it can cease to exist i.e., existence is not necessary with respect to its essence in the same sense that oddness is intrinsic/necessary with respect to the essence of number 3. Since you can suppose anything without entailing a contradiction then that thing is possible in itself.

Second, The universe is composite of its parts, it subsists through its parts. so it's causally dependent on them and therefore contingent.

Third, the parts of the universe are susceptible to corruption and generation, coming to be and ceasing to be, they are being caused, and they have a beginning of their existence, so they're contingent. since the parts of the universe are contingent, the universe must be contingent. Otherwise, the universe would have to be existent although its parts hadn't been existent. and that's like saying that the clock as a whole is necessary but its parts are contingent Despite the fact that the clock isn't anything other than its parts. so if its parts are contingent the clock must be contingent. if its parts are causally dependent the clock must be causally dependent. if its parts are CREATED then the clock is CREATED.

Fourth, The universe is composite of substances and accidents [e.g., aggregation, segregation, heat ... etc]. Accidents need substances to exist. so they're Possible in themselves. Since they're possible then they would need a cause.Now, they would be caused either by: a)the substances OR b)something else. if it's the former, then these substances are causing by either: a.1)their choice OR a.2)their nature, If it's the latter then the aggregated particles cannot be segregated neither can the segregated particles be aggregated, and that is known to be false. and it's absurd to say that they can choose. so accidents must be caused by something else. Now this something else is causing either: b.1)by necessity OR b.2)by choice. it cannot be the former for the same reason of (a.2), so it must be causing by choice, then the accidents would be CREATED i.e., have a bgeinning (because choosing to do something precedes that something). but since the substances do not exist separated from accidents, and accidents have a beginning, then the substances must also have a beginning. thus the universe is contingent.

Fifth, if the universe was eternal then, the bodies would have been either in motion or in rest eternally.
If bodies were in rest eternally then being in rest can't be ceased, but it's indeed ceasing so they can't be in rest eternally.

To Prove that we say:

If bodies were in rest eternally then the rest is either: a)substantial to the bodies' essence i.e., necessary OR b)possible. if it's the former then it would have been impossible for them to be in motion because essential properties cannot change, and if it's the latter then it would need a cause, and that cause is either: b.1)causing by its choice OR b.2)by its nature, if it's the latter then it implies that bodies are caused to be at rest by necessity and that affirms that there can't be motion in the universe and this is indeed FALSE. And the former entails that the body being in rest is something CREATED i.e., has a beginning, but we are supposing that it's eternal. and the same can be said for Motion. Hence, bodies can not be in rest nor in motion eternally. so the universe cannot be eternal let alone necessary. therefore it's contingent.

Sixth, The essence of the motion is composite of a state that had come to an end and another that has begun, so the true essence of motion entails the precedence by another, it Only gets to be understood through the transition between these two states. but the true essence of eternity entails not being preceding by another. For example:
............ ------A-----B-----C
For an Object to move towards C it would have to go through infinite states that must come to an end in order for the object to reach its goal. but what is infinite does not come to an end, that's a contradiction. so the transition is dependent on an impossible condition, and what depends on an impossible condition is itself impossible. so if there wasn't a starting point or an initial state at which the transition/motion can begin to occur then the motion would be impossible. Hence, the motion can't be eternal, therefore the universe can't be eternal. and whatever has a beginning is indeed contingent.

Seventh, For every one orbit which Jupiter completes Earth completes 12 times as many. but for A and B to exist eternally means that the number of their orbits must be infinite for each one of them. However, since it takes B 12 orbits in order for A to complete one orbit then the number of their orbits can't be identical. so they cannot exist eternally, for whatever is less than another by a finite magnitude is finite. and the same goes for all objects, their motion can't be eternal. and whatever has a beginning is contingent.
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Premise 4, most of the previous arguments refute the infinite regress and the eternal universe, so i'm gonna add a few more arguments.

First, If there were an actual infinite regress of causes then there would not have been an effect at all, If the existence of Z is caused by Y then Z cannot exist unless Y existed first. But for Y to exist the infinite number of prior causes must come to an end, Which is X. But the finitude of an infinite causes is contradictory.

Second, the infinite regress of contingent things does not actually solve the problem of the existence of contingent things at all, it just infinitizes the problem, that's a homunculus Fallacy. that would just be like if someone asks how Human beings exist while they could not have been existed and another answered that because other human beings caused them to. well, those other human beings fall under the subject of the question. infinitizing them would not solve the problem.

Third, it's not just that. actually, an Infinite regress of contingent things each one of them are the effect of the prior would just mean that there is no any contingent things in the aggregate. it would just be an infinite number of annihilated things. For example:
IF Z is caused by Y which is caused by X. then Z&Y cannot exist unless X existed first. but then the same goes for X and each object prior to it ad infinitum. so an infinite number of contingent things cannot exist unless an infinite number of contingent things existed first, but then the same goes for these infinite things and so on, ad infinitum. it's actually an infinite regress of searching for something that is already existent. but since nothing can be found to be existent. then there cannot be an infinite number of contingent things. there must be a starting point that is already existed, without depending on a prior existent thing, from which the existence began to emanate.

I'm gonna stop here with a quote by David Hume: "An infinite number of real parts of time, passing in succession, and exhausted one after another, appears so evident a contradiction, that no man, one should think, whose judgement is not corrupted, instead of being improved, by the sciences, would ever be able to admit of it."

NOTE: the argument was meant to be a proof for a god i.e., a necessary being that is one and has some attributes but then the post would have been too too long so I'm gonna refer to Another thread starting from the point number 8. and this comment and i may elaborate on them in the comment section.