"Not of blood" refers to the fact that there is no physical generation process by which we can become sons of God.
"Nor of the will of the flesh" indicates that we were not looking for God—we did not know what to look for. We knew about a lot about gods ("there are many gods," Paul says in I Corinthians 8:5), but we did not know what the God of the Bible was like. That is what we have to come to know. That is where eternal life resides—in knowing God (John 17:3). We did not know Him.
We did not know Him because we did not know what to look for. Even though we may have been searching for "God," we were not really searching for the God of the Bible, as we had no idea what to look for. We would never have looked for a God who commanded the keeping of the Sabbath or the holy days. Those are "Jewish." Our minds have been prejudiced in many different directions. We never would have looked for the God of the Bible.
John is showing it in another way—that we were not born by physical generation. We did not come to know God through any act of our own will, but rather it was something that came as a gift from God entirely.