When Jesus was baptised in the River Jordan, there were two animal references: the Spirit of God descended on Jesus in the form of a pigeon (most Bibles use the nicer sounding word “dove” but pigeons and doves are the same thing); and John the Baptist pointed out Jesus to some of his disciples saying, “here is the lamb of God”.
Pigeons and lambs are notably low status animals, which rest at the bottom end of the food chain. They were common creatures in that part of the world.
There is a long association of animals with deities in the history of religion. As a general rule, deities were associated with strong and powerful animals: lions, bulls, eagles etc. In the coming of Jesus, God was doing something quite different, and these two animal references express it. God does not come among us in power and strength; he comes among us in a lamb and pigeon sort of way - quietly, humbly, peacefully, gently and vulnerably.
God chooses to meet us on at lower end of life’s pecking order.