Is He to blame for us not listening, or for keeping our children and therefore, our descendants, from listening?
Yes, he is, because as the supposed creator of mathematics he would have infinite knowledge of the power of exponentials. He would easily have forseen that his method of revealing himself would literally leave billions of people on the planet who have never heard of him or been taught about him by their ancestors, just as they were never taught by their ancestors.
Knowing that this could be the only possible outcome of only a few of his children back in Adam's day or in Jesus' day being entrusted with spreading his message, it is perfectly fair and logical to say that God does not care about the human race. At best, you could say he only cares about the very few with whom he bothered to entrust his message. The rest of the human race he left to a small chance they would hear the message in what can only be described as a salvation "crap shoot".
Who says He never tried? Seems to me also that He has always revealed himself to those who have and exercise faith in Him. Now, through Christ.
He did try, with a few people. As for the rest, no he didn't try, because billions haven't heard of him or even had the opportunity. So, to paraphrase a scripture, "How can they put faith in one whom they do not know? And how can they know without someone to teach?" The answer is, they can't, as the scriptures themselves say. Where the scriptures are obviously incorrect is when they claim the good news of the kingdom will be preached in all the inhabited earth for a witness to all. This is not even close to happening and due to the aforementioned mathematical law of exponents, the chances of it happening grow less and less every year as the non-Christian population in the world outnumbers the Christian to a greater degree each year.
So, to sum up, God's method of revealing himself sucks (impossible since he is omnipotent), or he doesn't care about the human race (impossible since he IS love) or he doesn't exist and is just a creation of some long ago minds who didn't think their doctrines through to their logical conclusions.