As Dottard's answer states, the most common use of the article is anaphoric. This use makes something definite by saying in effect, "I am referencing the --- of which I previously spoke. In other words, Nicodemus is not using the article to indicate he is speaking of the God.
The anaphoric article is the article denoting previous reference. (It derives its name from the Greek verb , "to bring back, to bring up.") The first mention of the substantive is usually anarthrous because it is merely being introduced. But subsequence mentions of it use the article, for the article is now pointing back to the substantive previously mentioned. The anaphoric article has, by nature, then, a pointing force to it, reminding the reader of who or what was mentioned previously. It is the most common use of the article and the easiest usage to identify.1
Nicodemus is a Jew and is speaking to another Jew. He sees no need to make an initial reference to the God. Since both are Jews, Nicodemus takes for granted both he and Jesus have the same understanding of "God." He speaks as one Jew to another using proper grammar. First using "God" without the article and using the article when the term is repeated.
If anything, the passage presents Nicodemus as one who is fluent in Greek.
1. Daniel B. Wallace, Greek Grammar: Beyond the Basics An Exegetical Syntax of the New Testament, Zondervan, 1996, pp. 217-218