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Josh doesn't mean G-d in Hebrew, rather it relates to the verb meaning "to save, to redeem". Thus if your hypothesis is correct, the meaning of the name would be "G-d will save my people" , which actually makes sense.
Interestingly enough, even though both the prefix "Josh-" (ye'hosh-) and the suffix "-ami" are pretty common in biblical names, their combination is not a biblical name.