There is some information relevant to this question with regard to the Magi’s beliefs about stars in Did the Wise Men see the Star of Bethlehem at the east?
I will copy some points I made in my answer to that question, and seek to apply them to this one.
The Magi were astrologers, likely of the Zoroastrian tradition. They believed that Jupiter represented a new king; Saturn the old king. When both planets came together in planetary conjunction, that would signify a change of ruler to them. This happening in Pisces would speak to them of Israel as they associated Pisces with Israel. An article on this was in 1 September 2009 ‘Weekend’ magazine, reviewing a BBC2 documentary on Christmas Eve that year. It gave an explanation to that effect, by David Hughes, Professor of Astronomy at Sheffield University, about a rare triple conjunction, three years before Herod the Great’s death. The first conjunction, he said, was in May, giving them plenty time to plot the next two conjunctions (in September and November) and travel the very long distance to Jerusalem (over which the second conjunction appeared) at the time of Jesus' birth. The Bible shows a time gap between Jesus’ birth and the arrival of the Magi. There was also a little-known census that year, written about by 5th century historian Orosius. This triple conjunction seems to tick a lot of boxes.
The significance of this with regard to whether the Magi had an attitude of worship towards the infant lies in their belief that the planetary alignments that year heralded the birth of a new king of Israel. They knew Herod the Great was the current king and – given his gruesome track-record with real or imagined rivals – knew that to present gifts fit for a king to this infant could put them at odds with Herod. Yet they set out on a huge trip with gifts for a king. They believed that following the conjunction would lead them to this new king of Israel. Quite possibly at that stage, they had no thoughts other than to render homage to a new-born king.
Yet, by the time they’d diplomatically negotiated Herod’s territory, paying him a courtesy call (to ensure he didn’t suspect them of being spies, no doubt), they had learned from the Jewish wise men at court of ancient prophecies about a Messiah to be born in Bethlehem. One could suppose that knowledge of prophecies would up their view of this new king. No ordinary king this! A Messiah-King! Herod sent them to nondescript Bethlehem. That was when the final stage of the conjunction gave them the most accurate non-sat-nav pinpoint destination location, possibly in all history. The exceptionally bright heavenly light stood still above one particular house. That sight caused them to “rejoice with exceeding joy” (vs. 10) as they found the child with his mother.
But it was after they had rendered obeisance to this new Messiah-King that the full impact of the divine hit them. Then they were “warned of God in a dream that they should not return to Herod.” Surely that would convince them that they were dealing with the divine? They obeyed God and returned to their country by another way (vs. 12).
It seems that although they set out intending to honour a new king of Israel, by the time they left Herod they knew this was a prophesied Messiah-King so a sense of worship may have been gripping them once they were miraculously directed to the actual spot, and once God had spoken to them in a dream, they would be convinced of the divine nature of this one.