Does this sentence make sense, and does it mean that you will reach a place earlier than someone else? Or would you have to say "ahead of you" or the aforementioned "earlier than you"?
I will be there before you.
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before you makes sense and is completely idiomatic, probably more idiomatic than "I'll be there earlier than you". One of the meanings of before is "at an earlier time", and this is an example of using the word in that sense.
In fact, "I'll be in Scotland before you" is part of the lyrics of a famous song. (It's often written and sung as afore ye, which is archaic, but the words and meaning are essentially the same.)