No, that sounds kind of pretentious and just wrong, as though you looked through a thesaurus to find a synonym.
What is wrong with just using “believe”?
You wouldn’t use “cogitate” exactly this way either.
This word means “to meditate (on)”: https://www.merriam-webster.com/dictionary/cogitate - you would use this to describe thinking about something deeply and intently.
Not to describe something you think or know to be true.
“Cogitating” is more of an active process, and “believing” might be the result of “cogitating”.
In any case the word “cogitate” is not very common, and does sound pretentious to me.
“Meditate on” or “ponder” are preferable and more common (but still, none of these words are appropriate in this context).
ell.stackexchange.com/users/89131/Mixolydian
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.
ell.stackexchange.com/users/89137/SamBC
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.
ell.stackexchange.com/users/48962/RubioRic
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.
ell.stackexchange.com/users/90940/seschneck
If you're looking to be the opposite of pretentious, you could say I reckon that success solely relies on hard work.
ell.stackexchange.com/users/90938/erhweqrhweh
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’
ell.stackexchange.com/users/90956/Mbo42
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.
ell.stackexchange.com/users/90978/Pierre Saillard
In English, the word "Cogitate" is used almost exclusively for humorous or comic effect.
I've been cogitating whether to go for a perambulation, but I fear it may precipitate.
Means
I've been thinking about going for a walk,
but I think it's going to rain.
It's not that they aren't proper words, it's that they are ten shilling words used in a ha'penny sentence.
ell.stackexchange.com/users/22134/Ben
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.
ell.stackexchange.com/users/43851/Old_Fossil
I have been thinking about other ways to say "I believe" in an essay and I came across "cogitate". Do you think it would be appropriate to use this word in an essay's conclusion?  For instance, does this sound all right?        In conclusion, I cogitate that success solely relies on hard work.
Is "cogitate" used appropriately in "I cogitate that success relies on hard work"?
ell.stackexchange.com
<word-usage><word-choice>
ell.stackexchange.com/questions/199521
ell.stackexchange.com/users/83911/JustAnAmateur
The word “cogitate” is not very common, and does sound pretentious. Cogitating” is more of an active process, and “believing” might be the result of “cogitating”. Perhaps the phase "I speculate that" might be more appropriate. The word "cogitate" would rarely be used in the English language and would never be used to replace "believe" as it has a different meaning. 
Cogitate would not be used in this context. "Cogitate" means "to ponder" and not "to believe". The word "cogitate" is rarely used in English.