Bowing or prostration before a king or superior was a recognized act of homage in the ancient world. The Greek verb proskyneo can therefore describe reverence that is not necessarily worship offered to God.
For that reason this scene should be interpreted conservatively. Its Christological force grows when read as the first occurrence in Matthew's larger pattern, which culminates in worship of the risen Jesus.
Royal and pilgrimage imagery in passages such as Psalm 72 and Isaiah 60 describes nations and kings bringing gifts in response to God's redemptive reign centered on Zion and the Davidic king.
Matthew's scene echoes these expectations as Gentiles come to honor the king of the Jews, while Jerusalem's ruler reacts with hostility.
The magi do not merely acknowledge that a child has been born. They undertake a journey to find the king, rejoice at divine guidance, enter the house, fall before Jesus, and present valuable gifts.
The immediate scene can be understood as royal homage. Matthew, however, will repeatedly use similar worship language toward Jesus, including after manifestations of his authority and after his resurrection.
This is supporting rather than explicit evidence. The word for worship cannot establish Jesus' deity on lexical grounds alone.
Its significance is literary and cumulative: Matthew introduces Jesus as the proper recipient of extraordinary homage and never portrays him rejecting such devotion. Later scenes clarify the increasingly elevated identity of the one being worshiped.
The magi rejoice, worship Jesus, offer gifts, and obey God's warning not to return to Herod.