Other issues aside, the word order for that sentence is not quite right. I suppose if I were to translate what that says it’d say something like “Towards taking a trip I want the cosmos that inside”…
I’m gonna completely ignore the choice of words for this explanation, I’ll get to that later, but it’ll just confuse the grammar explanation if I bundle those I feel.
I guess my main advice would be to look up an article on Japanese word order (like this one), but generally:
The basic structure is SOV - Subject, Object, Verb. So you want to put the main verb (求める) at the end of the sentence.
The object is a clause - “taking a trip to space”. Particles (like へ) act on what comes before them, so when you want to indicate “to space” you’d say 宇宙へ, not へ宇宙 like you’d do in English.
Clauses are basically miniature sentences, so once again the verb (旅する) comes at the end, giving you 宇宙へ旅する as the full clause.
Because that ends in a verb you once again have to nominalise it, so it can become the object. You do that with の or こと (they’re equivalent for this purpose - there’s some nuance to when to use which but I won’t bother you with that for now, I’ll just use こと)
That gives you 宇宙へ旅すること as the full object of this sentence. Because it’s the object it takes the particle を after it (to indicate it as the object for 求める). That gives you 宇宙へ旅することを求める as a grammatically correct sentence. I’m not sure what その内 does in your original sentence, so I left it out here.
Now, on the choice of words:
求める is more about requesting something than about wanting to do something. For wanting to do something you can use the 〜たい conjugation, in this case 旅したい, to indicate you want to travel.
I’m not entirely sure 宇宙 is the right word for “space” in this sentence either, but I think it works, so let’s just keep it. Maybe someone else can weigh in on that, I’m kinda curious myself now.
So with that in mind, dropping 求める in favour of 旅したい you get 宇宙へ旅したい. You’ll notice the sentence has also been simplified a fair bit, since there’s no more need to nominalise a clause and use it as an object. In fact this sentence has no object, and the subject is implied to be 私 (or whatever is apparent from context) leaving us with only a verb clause. Japanese is funny that way, you can leave a lot of a sentence out if it’s already clear without mentioning.
I hope that’s clear! As before, if there’s a part you want to know more about feel free to ask
I tend to not include translations for my sentences but I’ll consider doing so, I think you’re not the first to mention that.
And I do try to help here from time to time, in no small part because explaining things helps me learn too - I’ll have to look up some information to form a clear explanation, occasionally coming across new stuff, and thinking about it differently helps it stick in my head too. I know there are others who do (and I’m by far not the most knowledgeable of the bunch, mind you) - but it’s all dependent on people being available and having the time and energy to do so, so there can be a lull in people helping.
Overall this is a very helpful community, and if there are specific questions you have you can go to the grammar questions thread or the non-grammar-but-otherwise-language questions thread. It’s not always clear where a question belongs, but when in doubt just pick one and you’ll get help either way, it’s not as if someone’s gonna bite your face off for posting something touching on grammar in the language questions thread
Also small bit of advice for you and other newbies: don’t be fooled by WK level. WK allows resets, and some of the most knowledgeable folks on here have some of the lowest levels (I’m definitely not one of them, just to reiterate that)