Non-Trinitarians who do not believe Jesus is God Almighty include Unitarians, Socinians, Arians, Jehova's Witnesses, etc. This would not include, supposedly, Modalists and LDS/Mormons.
The idea of atonement in the Old Testament was that a sinner would bring an offering to atone for his sin, and the death of that animal (and thus, its life) would take the place of the sinner's.
In his Temple, Its Ministry and Services, Alfred Edersheim wrote,
The fundamental idea of sacrifice in the Old Testament is that of substitution, which again seems to imply everything else—atonement and redemption, vicarious punishment and forgiveness. The firstfruits go for the whole products; the firstlings for the flock; the redemption-money for that which cannot be offered; and the life of the sacrifice, which is in its blood (Lev 17:11), for the life of the sacrificer. Hence also the strict prohibition to partake of blood. Even in the ‘Korban,’ gift (Mark 7:11) or free-will offering, it is still the gift for the giver. This idea of substitution, as introduced, adopted, and sanctioned by God Himself, is expressed by the sacrificial term rendered in our version ‘atonement,’ but which really means covering, the substitute in the acceptance of God taking the place of, and so covering, as it were, the person of the offerer.
Now, this would be a 1:1 relationship, i.e. one sinner, one animal. If Jesus is just a man (or even an angel, another created being), even if he be a sinless man (just like the animal was sinless and was offered as an atonement), how can Jesus effect atonement for all of humanity (John 1:29) rather than just one person?