Clearly, a child can not be the father of a man. In this poem, Wordsworth is speaking of his past self (as a child) being the father of the man he is at the present time and/or the man he will be in the future. The younger Wordsworth did not give birth to the older Wordsworth. But the younger Wordsworth did live before the older Wordsworth. This is the same thing as saying my eleven year-old self is the father of my thirty year-old self. That is to say, my eleven year-old self developed over the years to produce my thirty year-old self. This is a paradox or a stretch of an analogy which would compare a father "producing" his child to my past self producing my older self.
So, the child is the father of the man in linear terms; the child exists, in history, prior to his adult version. But there is more to say about this idea in the context of the poem and some of Wordsworth's other work. Wordsworth also implies that the adult can learn from his younger version of himself. When he was young, he was awestruck at beauty in nature (such as a rainbow). As an older man, he is still awestruck. He has learned to appreciate these things. He hopes that he will continue to experience nature in this way, to continue to experience nature as he did, as he learned, as a child:
So be it when I shall grow old,
Or let me die!
The Child is father of the Man;
And I could wish my days to be
Bound each to each by natural piety.
Just as he wants to continue to revere (piety) the beauty of nature as he grows older, he also wants his future self to revere his prior selves' experiences. In other words, he wants his future days to be bound to the same reverence of nature that he experienced in his prior days. Note that wording that the child is "father of man" (not "the" father of man).
In "Lines Composed a Few Miles Above Tintern Abbey," the speaker (Wordsworth) expresses a similar, although somewhat different, sentiment. He realizes that he will not have the exact same reaction to the beauty of nature as an older man but believes that in his wisdom he will appreciate it more:
And I have felt
A presence that disturbs me with the joy
Of elevated thoughts; a sense sublime
Of something far more deeply interfused, (93-96)
Although he will experience things differently as he grows older, he thinks and hopes that his future experiences will be as profound, albeit different, as his experiences as a younger man. In much of Wordsworth's poetry, he expresses the desire to continue to see the world with the same wonder that a child sees it.