Philo of Alexandria (20BC-50AD) was a Jewish philosopher, whose writings were largely lost to mainstream Judaism. Part of the reason I find him so interesting is that he had first hand knoweldge of the temple. Here is his description of Rosh Hashana - The Eight Festival of the Year:
THE EIGHTH FESTIVAL
XXXI. (188) Immediately after comes the festival of the sacred moon; in which it is the custom to play the trumpet in the temple at the same moment that the sacrifices are offered. From which practice this is called the true feast of trumpets, and there are two reasons for it, one peculiar to the nation, and the other common to all mankind. Peculiar to the nation, as being a commemoration of that most marvellous, wonderful, and miraculous event that took place when the holy oracles of the law were given; (189) for then the voice of a trumpet sounded from heaven, which it is natural to suppose reached to the very extremities of the universe, so that so wondrous a sound attracted all who were present, making them consider, as it is probable, that such mighty events were signs betokening some great things to be accomplished. (190) And what more great or more beneficial thing could come to men than laws affecting the whole race? And what was common to all mankind was this: the trumpet is the instrument of war, sounding both when commanding the charge and the retreat. ... There is also another kind of war, ordained of God, when nature is at variance with itself, its different parts attacking one another. (191) And by both these kinds of war the things on earth are injured. They are injured by the enemies, by the cutting down of trees, and by conflagrations; and also by natural injuries, such as droughts, heavy rains, lightning from heaven, snow and cold; the usual harmony of the seasons of the year being transformed into a want of all concord. (192) On this account it is that the law has given this festival the name of a warlike instrument, in order to show the proper gratitude to God as the giver of peace, who has abolished all seditions in cities, and in all parts of the universe, and has produced plenty and prosperity, not allowing a single spark that could tend to the destruction of the crops to be kindled into flame.
Though in this text Philo does not mention any concept of "New Year" he does make a passing reference to it elsewhere. Weirdly, his universal interpretation for the Shofar ("Trumpets" which is how the Pentatauch translates it) is negative. We hear the trumpets - a sound of war - to give thanks to G-d for giving peace.