Did the Holy Spirit move into Jesus during and after His baptism for the first time?

The Gospels record that at Jesus’ baptism, the Holy Spirit descended on Him like a dove (Matthew 3:16, Mark 1:10, Luke 3:22, John 1:32). Immediately afterward, we read that the Spirit led Him into the wilderness to be tempted (Matthew 4:1, Mark 1:12, Luke 4:1). Does this mean that the Holy Spirit entered or moved into Jesus only at His baptism, and then guided Him into the wilderness? Or should the descent of the Spirit be understood differently, since Luke 1:35 indicates that Jesus was conceived by the Holy Spirit and therefore already had a unique relationship with Him before baptism?