The OT usages of "children" also means "sons" indicating a child-father relationship between Creator and man (Gen 6:2; Heb 12:9) and esp. between Israelites and God Deut 14:1), but my intention is to explain the differences between the OT and NT usages of this doctrine.
In the OT it was as a child-father relationship but was not a practical (in practice or performance) relationship, which was not possible until the Holy Spirit was given (John 7:39) i.e. “If then I be a father, where is mine honor” (Mal 1:6)? I refer to a child in a true sense—by the Spirit (Rom 8:14, 15; Gal 4:6; 1 John 3:2), not in a false sense (Rom 9:8). This is “by adoption, secretly (Eph 5:32) in God's predestination, and in the covenant of grace; and openly in regeneration, through faith in Christ, and by the testimony of the Spirit” –JG (Rom 8:16).