The first form is fine.
The general form "because X, Y" means that X gives a reason why Y is true, or happened, if it is an action as in Emily Dickinson's:
Because I could not stop for death— / He kindly stopped for me—
It is of the same meaning as:
Death kindly stopped for me because I could not stop for him.
It lacks not just the poetry of Dickinson's form in terms of how it scans, but the switch in the ordering of clauses gives a different emphasis and order of thoughts and so is rhetorically inferior (so much for the schoolroom rule against starting a sentence with because).
Now we can always deny anything we can state, and we could say "Because X, doesn't mean Y" or "Because X, not necessarily Y" etc. as per:
Because you're paranoid doesn't mean that they're not after you.
But this is vague. We're denying the causal relationship, but "doesn't mean" can be lost in the reading; it doesn't stand out much, so it's easy to "slide over" in reading or listening. What we want is to stress that we are limiting the because, and for that we use just:
Just because you're paranoid doesn't mean that they're not after you.
Not only does this use of just do this when we consider it without knowledge of idioms, it's also a very common idiom to use "just because" in this way. (Incidentally, Oxford and Cambridge both have "just because" sentences in their examples for because while Macmillan lists "just because" as a phrase under just).