Q. I once held the view that Jesus to be truly human had to have at least the option of sinning. I changed my view when I was taught that Jesus didn’t have a sin nature like us, thinking that without this fallen nature, it would have been impossible for Him to sin. But, the thought came to me that Adam and Eve didn’t have a sinful nature at first, yet they sinned. So, any thoughts?
Your question bears on the issue of whether Jesus on earth was “not able to sin” or instead “able not to sin.” Christians of good will with equal commitments to the authority and inspiration of Scripture hold different views about this. I personally believe that it was not the case that Jesus was “not able to sin” while he was on earth. I believe he was instead “able not to sin” (your original view). But this was not because he did not have a fallen nature or sin nature.
Rather, to borrow the language of Augustine, once we come under the influence of original sin or a fallen nature or sin nature, we are “not able not to sin.” We may do some good and right things in life, but we will also sin, inevitably. We need to be born again, regenerated, so that we will have a new nature that is no longer under this constraint.
Without original sin or a fallen nature, we would then be in the same situation as humans before the fall. To quote Augustine further, in that situation, people were both “able to sin” and “able not to sin.” That is the radical nature of human freedom. So Adam and Eve sinned, even though they didn’t have a sinful nature at first, because they were “able to sin,” in addition to being “able not to sin.”
So what about Jesus on earth? I would describe him as “able not to sin,” and that was true of him because he was completely yielded and obedient to his heavenly Father and because he lived his life in the power of the Holy Spirit. This was true of him to such a degree that I would actually hesitate to describe him as “able to sin” while on earth, although technically that was a possibility, in my view. What I mean is that while it was a theoretical possibility, it was not an actual one, given how absolutely devoted he was to God.
In that way Jesus sets an example for us. We, too, are “able not to sin” when we yield our wills completely to God’s will and live in the power of the Holy Spirit. Jesus did this consistently for a lifetime, which is far more than we can realistically hope for ourselves, but we can at least hope for more and more occasions on which we find that we are “able not to sin” as we are yielded to God, obedient, and Spirit-filled.
And we can also anticipate the wonderful time when, glorified in the presence of God after this life, we will be truly “not able to sin.”
Good Question 
I think some things we may not know, at least, not in this life. However, both were tempted. One sinned, Adam, and our Lord and Savior did not. I don’t know it does much good to overthink.