Jesus Christ received the Holy Spirit when he was 30 years old. Wasn't that supposed to take place much earlier?
There are a few angles to answer your question from.
First the Eternal Son of God, who existed before being incarnated into a baby child through a virgin can never be said to not have the Spirit for the Trinity if One God, Father, Son and Spirit. This is the basic view of God within Christianity.
Second, when the Eternal Son was incarnated the human nature that he incorporated into his person could never be said to not have the Spirit for the Divine nature and the Human nature are inseparable in his person forever.
Third, as a man Jesus needed additional supplies of the Spirit to resist sin and to obey all that his Father has given to him to do. In this sense of ‘needing’ the Spirit to live a holy life as a man in communion with his Father he must have to be fully human. We can see even in what little record we have of Jesus as a child where the Spirit was mighty in him. In Luke 2 Jesus was separated from his parents and was later found engaging the teachers in the temple courts. When they rebuked him for getting lost while they were worried he said “Didn’t you know I had to be in my Father’s house?”. This implies at an early age he was already deeply aware of his fellowship with the Father which is by the Spirit. It is then added that:
This obviously implies that the Spirit of God was causing the boy Jesus to develop in ‘spiritual’ wisdom, not just the human kind, meaning the Spirit was deep at work within him.
It is from this third aspect that your question is based and the answer is simple. Of course Jesus as a man always had supplies of grace from the Spirit and communed with his Father, but it was not until his official ministry in preaching the gospel was inaugurated that he received the Spirit in an extra and unusual manner in order for him to perform his earthly ministry.
This is not only true of Christ but of all Christians that ‘receive the Spirit’. It is not something that happens once but over and over again and our needs require and God’s grace supplies.
As you have rightly said, Jesus was conceived of the Holy Spirit and so is John the baptist. They were filled with the Holy Spirit from their mothers' womb
As I understand it, the Spirit came on Jesus not to fill him but to reveal him to John
And for the baptism - to fulfill all righteousness. If Jesus did not do it, I think baptism in Christianity would have been history