When did Jesus begin His ministry?

Luke 3:23 states that Jesus was 30 years old when He was baptized by John the Baptist and this was when His ministry began.  Before this, Jesus did not reveal anything to anyone about His being the Messiah.  John the Baptist was to be the one who publicly began pointing the way to Jesus (John 1:23).  The sign of the Holy Spirit descending upon Jesus was only for John the Baptist and he began telling everyone what he saw shortly after this (John 1:32-33).  Before His ministry began, Jesus did ask and answer questions in the temple at age 12 (Luke 2:46-47).  But in this He was not revealing to the public that He was God in the flesh (John 1-3; 14), but a reminder to Mary and Joseph as to who He was (Luke 2:48-49).  Jesus also did not do any miracles until His ministry began (John 2:1-11), which goes against heretical claims He did so as a child.