Just as there might different paths through a forest, each bringing with it a different experience, there is no one correct way of understanding "Thirteen Ways of Looking at a Blackbird." The clue is really in the title—there are multiple ways of looking at the world (indeed, the number thirteen seems to have been picked arbitrarily by the speaker) and accordingly the poem doesn't resolve to one single, overarching perspective on blackbirds.
Rather, the poem suggests that meaning is as much constructed by the reader's experience and understanding of the poem as anything else, which foregrounds one of main ideas: that knowledge, truth, and beauty are inevitably filtered through human perspectives (though the senses and the mind). It's worth noting again, before setting off into the depths of this poem, that Stevens's himself described it as a series of "sensations," a word that accurately describes the fleeting, elusive quality of each of the poem's thirteen sections (which Stevens also thought of as mini-poems in their own right).
If human perspective and its limitless possibilities are the poem's main theme, the first stanza also introduces the other consistent thematic focus: the natural world. The first line describes an image of epic natural scenery—indeed, twenty mountains would probably stretch the limits of human perception in terms of how much the eyes can take in.
The unrelenting /n/ and /ng/ consonance of the first two lines represents the physical and visual dominance of the mountains:
Among twenty snowy mountains,
The only moving thing
Line 3 contrasts the vast, imposing presence of the mountains with a much smaller—yet no less wondrous—expression of the natural world: the moving "eye of the blackbird." Amongst this vast stillness, the blackbird's eye is scouting its environment—perhaps suggesting nature's ability to adapt and survive.
Notice the way that in three short lines the poem has already set up two completely different perspectives: the telescopic vision of twenty mountains, vs. the zoomed-in perspective on the blackbird's eye. Already, then, the poem is challenging the reader to consider the fundamental role the perceiver—the person reading the poem, looking at the bird—plays in any act of perception.