Q. When did the worship of Jesus, as God, rather than Messiah, Lord, and Savior, begin? And by whom?
A. First I have to address the wording of the question. It could be asking when/whether Jesus came to be “God” or when “God” came to be re-signified as Jesus. There’s no evidence that Jesus replaced God or overwrote God (so to speak), at least not in the first couple of centuries. Subsequently, there have been Christians for whom God was Jesus, pure and simple. But that’s not what scholars find in the earliest centuries.
But I presume that you actually mean “when and where did Jesus first come to be reverenced as somehow really sharing in God’s status, or glory, and so the rightful recipient of worship along with God?” This has been a contested question for at least a century or more. Pretty much everyone is agreed that Jesus didn’t receive worship during his ministry. The key questions contested are how soon and where after Jesus’ crucifixion did it begin.
One view is that the worship of Jesus as divine first appeared in the later decades of the first century, and likely in Gentile Christian circles (see the works of Dunn, Casey, and McGrath). But, over the last century or so, most scholars have agreed that the worship of Jesus as the divine “Lord” (Greek: Kyrios) began very early, within the very first years after Jesus’ crucifixion.
In an influential book Kyrios Christos, Wilhelm Bousset took this view, contending that this was the form of Christian faith that the apostle Paul was introduced to after his “conversion,” typically dated ca. 30-35 C.E. But Bousset also insisted that this treatment of Jesus as divine Kyrios couldn’t have happened in a thoroughly Jewish context (in which monotheistic concerns dominated), and so he placed the development in diaspora sites such as Antioch and/or Damascus (in Syria), where, he posited, pagan models of the divinization of heroes could have been influential.
In the last few decades, however, a growing number of scholars have argued that the earliest expressions of cultic reverence of Jesus as Lord were, indeed, in the very earliest years (likely earliest weeks or months) after Jesus’ crucifixion, but (contra Bousset) initially in Jewish circles of the Jesus-movement and in Roman Judaea (Palestine). Among the relevant works is my own One God, One Lord. Without getting into the details, my emphasis is on the constellation of specific devotional practices that expressed a reverence for Jesus as divine Lord.
Paul’s letters give every indication that the kinds of Jesus-reverence that he knew and affirmed were also practiced among Jewish circles of believers. The Aramaic liturgical expression, “Maranatha” (= “O/our, Lord, come!” cited in 1Cor 16:22), is one of several pieces of direct evidence that Jewish, Aramaic-speaking believers invoked the risen/exalted Jesus as “Lord” in their corporate worship gatherings. The basis for this remarkable development was apparently the convictions that God had exalted Jesus as “Lord,” that Jesus now shared God’s glory, name and throne, and that God now required Jesus to be reverenced accordingly (e.g., Phil 2:9-11).