You know at least one thing about God. You know He exists. Do you think it's possible to know more about Him without understanding the full scope of His being?
"I have no problem with thinking this. Don't you think, that after all these years that humans have populated this earth, that if we were supposed to, or were able to know, this question would have been answered by now?"
I'm not sure which question you are referring to, but as a Christian (arrogance warning) I do claim to have an answer to the question. Of course, since I am human, my answer is incredibly short of His complete nature but it is an answer nonetheless.
"I am not so arrogant as to assume I can understand God. "
I hear what you're saying and I know that I, as all people who claim to know the Truth, come off as arrogant. Ten years ago I wouldn't have made any claims as to knowing the Truth, or even Acknowledging that there is a Truth but i've had experiences (improvable of course) that have changed that way I think about God and Truth. Because of these changes I can claim to know that Truth without feeling arrogant at all.
"Why should I spend my short time on earth striving for something that I can't have, or would even understand?
I think you can get to know Him...and I think you can understand Him more than you think possible.
"I certainly don't want God to leave me alone, that is why I thank Him daily for letting me be the way I am."
Have you ever asked Him who Jesus is?