There have been various theories regarding the origin of the nomina sacra.
Ludwig Traube (Nomina Sacra. Versuch einer Geschichte der christlichen Kürzung, Munich 1907, p.36) proposed that nomina sacra began among Greek-speaking Jews who sought to imitate the Hebrew consonantal writing of the divine name by omitting the vowels of theos.
A.H.R.E. Paap (Nomina Sacra in the Greek Papyri of the First Five Centuries, Leiden 1959, pp.119-27) agreed that the contracted form was an imitation of the consonantal spelling of the tetragrammaton.
Schuyler Brown ("Concerning the Origin of the Nomina Sacra", Studia Papyrologica 9 (1970) pp.7-19) proposed that kurios was first used as a reverential way to render the Greek substitute for the tetragrammaton in Christian copies of the Greek OT.
Kurt Treu ("Die Bedeutung des Griechischen fur die Juden im romischen Reich", Kairos 15, 1973, pp.123-144) maintained that the nomina sacra initially included both theos and kurios to distinguish them in Greek texts where they served as translation equivalents for the tetragrammaton.
Colin H. Roberts (Manuscript, Society and Belief in early Christian Egypt, London: The British Academy, 1979, pp.35-48) argued that the nomina sacra are a Christian innovation reflecting the influence of Jewish reverence for the name of God, reshaped under the impact of Christian religious convictions.
George Howard ("Tetragrammaton in the New Testament" Anchor Dictionary of the Bible, vol. 6 (New York, 1992), pp. 392–393) argued that kurios and theos were the initial nomina sacra,
"first created by non-Jewish Christian scribes who in their copying the
LXX text found no traditional reason to preserve the tetragrammaton"
and may have considered the contracted forms of these words "analogous
to the vowelless Hebrew Divine Name".
Larry Hurtado ("The Origin of the Nomina Sacra: A Proposal", Journal of Biblical Literature, Vol.117, No.4, 1998, p.663) states:
But it seems likely that Jewish reverence for the divine name, and particularly the
Jewish
practice of marking off the divine name reverentially in written forms,
probably provides us with the key element in the religious background
that early Christians adapted in accordance with their own religious
convictions and expressed in the nomina sacra.