I would like like to translate "everything started here" in Latin. Would omni coepia hinc work?
I’m not quite sure how you arrived at your final result; omnī is the ablative singular of omnis, omne, which doesn’t make much sense if you are trying to convey the word everything; coepia, well, I’m not really sure if it even exists; and hinc means hence, hencforth, from here, etc., not here. All together, the phrase you’ve got is completely unintelligible.
Go for this instead:
Omnia hīc coepērunt.
If you want to avoid potential ambiguity regarding the subject of coepērunt, you can always opt for a passive phrase as well (thanks to @SamK for pointing this out to me):
Omnia hīc coepta sunt
You can rearrange the word order in either of these phrases to whatever emphasis or style suits you; they are simply a starting point.
'Everything' needs a Neuter Plural ending; so, omnia, omnium, or omnibus.
Coepi is a good word, but it is tricky: it looks like a past tense, and behaves like a past tense, but its meaning is present tense. Coepi = I begin. So an 'extra' past tense has to be added. Omnia coeperunt =Everything begins
coeperant =began. Lewis and Short (Tufts) coepio section II (But notice the ambiguity mentioned by Sam K in the notes.)
Hinc means 'here.' But I would choose
abhinc =from here.
Next, put the words in Latin order. Usually the verb goes last because that is the most significant position. But if you want to emphasise another word, put that last.