When you say "the first Greek dictionary" do you mean a dictionary of ancient Greek or a dictionary of modern Greek? Do you mean a Greek-Greek dictionary or a dictionary that translates Greek into another language?
If you are referring to ancient Greek, the first "dictionaries" that appeared were glossaries that explained words from Homer's works. These glossaries did not have alphabetical order and were particularly developed in the times of the Sophists.
In case you refer to modern Greek, things are more complicated. Until 1976 there was an artificial bilingualism in Greece. The official language of the state (known as "katharevousa") was different from the live spoken language,(known as "dimotiki".) So there are dictionaries that explain the spoken language (demotic) in terms of the katharevousa. These are quite difficult to understand and not recommended for someone that studies modern Greek now.
If you refer to the first Greek-Greek dictionary that explains dimotiki in terms of dimotiki (which was established as the official language of the state in 1978), then the first is the following: E. Kριαράς, 1995. Λεξικό της σύγχρονης ελληνικής δημοτικής γλώσσας. Aθήνα: Eκδοτική Aθηνών. (E. Kriaras, Dictionary of the modern Greek language. Athens, Ekdotiki Athinon.)