How possible is it that the Septuagint / LXX wasn't specifically quoted in the NT?

Couldn't it be possible that the NT writers quoted from a Hebrew or Aramaic Old Testament, and that the Septuagint was transliterated afterwards, or that the NT was later translated to match the Septuagint? The reason why I ask this is because I can't really seem to find much proof of the age of the Septuagint. The two arguments for the authenticity of the Septuagint seem to be "the NT writers quoted from the Septuagint" and the anecdote of a Jew named Aristobulus, who mentioned that the Law had been translated into Greek under the reign of Ptolemy. Don't Jews refer specifically to the books of Moses as the Law? And wouldn't it be a big stretch to assume that he is truly speaking about the Septuagint being translated during the reign of Ptolemy? Yet this is what many advocate to be true.