the universe is indeed contingent,

I assume you support this with the rest you write. (we shall see!)

the mind judges that it could not have been existed and could cease to exist, it's admissible in the mind to say that the universe could not have been existed without contradiction.

- Sure a mind can judge that, my mind also sees the possibility that the universe at one point did not exsist and may cease to exsist at one point in the future. Do I accept that as 100% the only possibility? No. because I have seen no evidence for that yet, I assume when you say "it" you mean universe.
- I agree it is "admissible" to the mind to say what ever you want. It is admissible to the mind I have 3 arms, its an unsupported idea presented to the mind, but it is admissible.

So far I see: you are saying the universe is contingent because you think it is, it is possible for you to consider the possibility that it is contingent. Because I possibly consider the possibility that Santa Claus is real does not make it real.

the mere conceptualization of its essence does not tell us something about its existence, it does not include its existence.

I assume again that "it" is the universe. I consider my self at least: "above average" when it comes to understanding the written word and I struggle to understand precisely what you are trying to say here. I can only guess what you are trying to say here is: "The simple idea of the universe, (as the idea thought up by human brain,) does not help us with defining or proving the universe in anyway, because its only an idea. <= I happen to agree.

the universe is nothing without its parts, it's complex/composite of its parts/units, and what needs/lacks/depends on its parts IS indeed contingent.

-I agree, you cannot have a universe if has a complete lack of any parts, then we are just talking about nothing. If a quarter of the universe suddenly winked out of existence, we would still have a universe, even if 99 percent of it was gone, there would still be a universe, greatly changed, sure but it would still be the universe. We could double it too. Same thing with your house example. We could subtract out rooms, gut out the plumbing etc, it would still be a "house" just one that lacks plumbing and additional rooms. I suppose if you removed walls and a roof, what is remaining would not be defined as a house, maybe a cave?
- I can agree all parts within the universe are contingent, it follows the rules of the universe. Chemistry/physics, atomic energy study etc all show everything has to have a cause. It looks like that cause is ultimately the big bang. BUT: the big bang we do not know if it has to have a cause. It did not occur "within" the universe and it's rules. The rule that everything has to have a cause or be "contingent." We do not know applies to before/outside the universe. I said this before, and you keep dismissing it. When we talk about the creation of the universe, the "rule of contingent" no longer necessarily applies. It might, it might not, we do not know because we can not study this "before or outside" the universe all we can study is the current visible universe, (limited by the speed of light.) We can not even hypothesis or theorize the "before" we have absolutely nothing to build a hypothesis or theory on other than our very limited imagination, (limited in the area of something we never observed or experinced.)

we see objects in the world starting to exist and ceasing to exist, and what its parts starting and ceasing to exist i.e contingent, as a whole, would not be necessary.

Uh, that goes against your own contingent argument. And the rules of the universe, nothing is created nor destroyed, within this universe, things just change states, at least that's the prevailing popular theory so far backed by evidence. (Some dark energy stuff humans are looking into now may change this popular theory if we want to include dark matter/energy as part of the universe.) I also do not see how this relates to you supporting your assertion that the universe is indeed contingent.

it's like saying the parts of a house needs to be built but the house as a whole doesn't.

I think I get what you are trying to say here, but the house analogy does not work here. I think an analogy of what I am trying to say is: When playing a game of chess, every piece is important, the board is important, and they are all bound by rules to make the game of chess work. However before chess board pieces were made, before the rules were made, the rules of chess did not apply. The rule that if you take the king = winning the game did not apply. Before the whole concept and all the pieces existed, there were no rules, no rule that if you take the opponents king piece that person "loses" all the rules are contained solely within the created concept of chess and the parts that make it work. Additionally all these rules only apply when the actual game of chess is being played and the players agree to the rules. They cease to apply after the game ends, just like they did not apply before the game began.