The first line of the poem creates an immediate sense of the speaker's separation from the place he's about to describe. This alienation is evident from the very first word, in fact: a powerful, dismissive "That." The word "That" gives readers a sense that the speaker is already standing at a remove from whatever he's describing. While his body might be in the country he's about to describe, he feels far away from it.
The sounds of this line are similarly telling. The sharp /t/ sound of "That" start readers off with a bang, but then the vowel sounds begin to slide and lengthen. Four variations of the /o/ vowel sounds appear in succession:
no country for old men
This combination of likeness and unlikeness (the sounds are similar, yet not quite the same) foreshadows the speaker's relationship to the country he feels himself to be so separate from. He will be able to see the world of the young from a position unlike that of its happy, lively inhabitants, but he also has a deep familiarity with their situation: he was, of course, once young, but is not anymore.
The sentence is strong and declarative: no commas or other interruptions soften it. It also sits uneasily next to the rest of the line it belongs to. After the strong caesura of the period following "men," the reader encounters the beginning of a new sentence: "The young."
Enjambment then separates "The young" from whatever it is that the speaker is going to say about them, so that those young people sit in isolation next to the first sentence's evocation of age:
That is no country for old men. The young
The reader immediately gets the sense that, whatever the reasons are that the country we're encountering is no good for old men, the young have something to do with it.