It just means that you're happy to meet someone that you have never met before. "Acquaintance" is someone you have met before, so "making your acquaintance" means that you are meeting someone for the first time. It can be said whenever you are meeting someone for the first time.
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August 17, 2016
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"started" is the past tense of "start", so to say, "why don't we started" does not make sense. The correct way is "Why don't we start". Once corrected, both sentences mean the same thing.
