Was Jesus anointed upon his baptism (Matt, 3:16-17) ?
Aside from the fact that being the 'Only Begotten Son' of God, in his pre-earthly existence and thus set apart from all other spiritual beings for special purposes, his true calling was to be an earthly one, in the guise of Jesus, the Christ (from the Greek 'Christos' meaning 'the anointed one', translated from the Hebrew word Masiah/Messiah).
To answer this question, as to whether Jesus became 'the anointed one' at his baptism, or at some other time, one needs to take note of Dan, 9:25 [NASB]...
"So you are to know and discern that from the issuing of a decree to restore and rebuild Jerusalem until Messiah the Prince there will be seven weeks and sixty two weeks; ...."
Messiah can also mean 'anointed ruler', and we are told in the above verse that he became thus at the end of the "...seven weeks and sixty two weeks", which was at his death, in the spring of 33 AD, - for an in depth exegesis on Daniel's '70 Weeks' prophecy, you can see my answer to the following question Are the 70 weeks of Daniel and Jeremiah prophecies about the Babylonian exile of the 6th century BC or about the age of the Messiah? - at the end of his 3 1/2 year ministry, which started with his baptism in the Fall of 29 AD. Consequently, although Jesus was initially anointed by the 'spirit of God', at his baptism, after the Father's thunderous proclamation...Matt, 3:16-17, that was not the 'ultimate' anointing, as this came after his death, when he fulfilled the 6th and final point of Dan, 9:24 "...and to anoint the most holy place", whereupon on arriving back into the heavenly realm, he sat at the right hand of God, in the 'Holiest of Holies', to begin his 'princely' rule. The 'kingly' rule, of course, being yet future.
It is worth noting Acts 13:32,33 at this point, in regard to Jesus' resurrection, subsequent to his anointing in the 'Holiest of Holies'...
32 "And we preach to you the good news of the promise made to the fathers,33 that God has fulfilled this promise to our children in that He raised up Jesus, as it is also written in the second Psalm, THOU ART MY SON; TODAY I HAVE BEGOTTEN THEE."
The above is a translation from the NASB, whereas other translations, as far as the capitalized letters are concerned, an example being within the NWT, say:-"You are my son, I have become your Father this day."
Both translations, of this final part of 33, are a little misleading. Jesus was BEGOTTEN of the Father in the beginning, as per 'John's prologue', but here 'BEGOTTEN' means 'of the dead' and 'the Father' is renewing his identification to the son (see Barnes' notes on 33). The Greek word 'gegenneka', in the NWT's Greek interlinear (KIT of the GS), translates this as 'have generated', meaning 'caused to arise or come about', "... son of me are you, I today have generated you.", which IMO is a much better rendering of the original writer's (Paul's) intent.