Tjyylli

Firstly, it's pretty rare to use cogitate at all. Using any word related to it, the most common is "cogitation", the action noun for the act of cogitating.

Second, think has two main senses in English. Most of us native speakers don't even necessarily realise it, but if we learn a language that has separate words for the two, like French, it kind of clicks. In French, there is penser, the active sense of think, where we might say think about, and croire, the stative sense of think, which is closely matched in sense to believe (though clearly with some difference).

Cogitate is a close match to penser, not to croire. It means the act of thinking, pondering, and so on. You might, if you wished to be pretentious, say:

Let me cogitate on that a minute.

You can't say what you want to say. It doesn't make sense.

I agree with Mixolydian, "cogitate" sounds pretentious and doesn't fullfil exactly your intention.

I don't know where you have found that word but what about checking the Oxford Thesaurus?

Let me suggest some alternatives

In conclusion, I think that success solely relies on hard work.

In conclusion, I consider that success solely relies on hard work.

In conclusion, I'm of the opinion that success solely relies on hard work.

As Mixolydian states, cogitate is more about meditation or consideration of something. However, you could use it by rearranging your sentence a bit:

After some cogitation, I conclude that success solely relies on hard work.

This implies that the conclusion was reached after the cogitation.

If you're looking to be the opposite of pretentious, you could say

I reckon that success solely relies on hard work.

I think you are trying to suggest that your conclusion is based on some careful consideration. So you might try:
In conclusion, I determine (or have determined) that success solely relies on hard work.

From the OED.

Verb

Ascertain or establish exactly by research or calculation.
‘the inquest is entrusted with the task of determining the cause of death’
with clause ‘the point of our study was to determine what is true, not what is practicable’

The word "cogitate" means to ponder on think about intently. A deliberate thought process whereas "believe" is relative to a matter of faith or speculation. Perhaps the phase "I speculate that" might be more appropriate.

In my native French language, the verb "cogiter" has specific meaning.
It is used when one experiences deep, chronical thoughts about a subject. It often refers to an unpleasant feeling, an obsessive thinking, which sticks to you for a relatively long period.

So when I read

In conclusion, I cogitate that success solely relies on hard work.

I get a weird feeling about your sentence's time consistency.

In formal writing for essays I would avoid using "I think" or "I believe" or "in my opinion". If you are writing the essay, then it is understood to be your original thought and your beliefs or opinions. These phrases are just filler. Whatever you are saying before should lead to the logical conclusion that success relies solely on hard work. Even the phrase "in conclusion" looks like filler to me without context.

For example:

1. This is my dog spot.


2. Spot is a very hard worker.


3. Spot became very successful after working hard for a long time.


4. Spot sacrificed his free time to work.


5. Spot's success is due solely to his hard work.

In this example, you can see how your fillers can be placed anywhere and not really change the meaning:

1. This is my dog spot.


2. 
   I believe he is a very hard worker.


3. 
   In my opinion he became very successful...


4. 
   I think he sacrificed a lot...


5. 
   In conclusion, I believe that Spot's success is solely due to hard work.

When writing an essay, you should present facts and evidence, and let conclusions arise from the flow of the logic. If it's fiction, then you can write such a narrative but it would be odd to include yourself. Even if it's an opinion piece, then you would still avoid any kind of narrative, and instead present facts to support your own opinion, but not in a way that ties it to yourself.