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I have a Blue Card visa from Germany, which I just got. In my first entry to Germany, I will book a transit plane ticket from my home country to Greece then Berlin.
If I want to leave the airport during the transit time, in Greece, can I do that freely, or I won't? Note that I didn't enter Germany before since the visa got issued.
Yes, you can leave the airport. At least, that is true as far as immigration law is concerned; whether you will have time to do so is another question.
In any event, your flight from Greece to Germany is an "internal" Schengen flight, without border controls, so you will clear the Schengen passport check when you arrive in Greece. This would be true even if you had no intention of leaving the airport.
