"Alone" begins with a speaker recalling the loneliness and isolation of his childhood. From the very beginning of his life, he says, he's sensed that he is different from those around him, and that his difference stems from the way he sees the world.
The parallelism in the first three lines helps to make that point clear:
From childhood's hour I have not been
As others were— || I have not seen
As others saw— || I could not bring
These similarly-shaped lines suggest that the way the speaker is and the way he sees the world are closely related. And the caesurae here—strong dashes—make it sound as if it's pretty hard for the speaker even to talk about how lonely and misunderstood he's felt. It's as if he's breaking off mid-thought, trying to communicate his extreme feelings of loneliness—but not sure, even now, that he'll be understood.
Altogether, the first four lines really set the tone of the poem. There is no doubt that this is an intensely lonely speaker who desperately longs to connect.
But perhaps there are also some consolations in this loneliness. These lines are subtly musical: they use singsongy rhymed couplets and harmonious /n/ and /m/ consonance:
My passions from a common spring.
These gentle, musical sounds perhaps suggest the speaker has found a silver lining in his loneliness and difference. His unique way of seeing the world might make him special as much as it sets him apart: it might, in fact, have made him a poet!
He may not have been able to draw his "passions" (or deep feelings) from the metaphorical "common spring" that most people shared. But, as the poem will show, his passions might come from an even deeper and wilder source.