What quotes in the beginning of the Odyssey prove that Odysseus can overcome obstacles to reach his goal?
From the very opening of Homer's Odyssey, the epic poet indicates that the title character has the ability to reach his ultimate goal of returning to his native land of Ithaca.
The first line of Homer's Greek text contains the word polytropon, which means "versatile." A.S. Kline translates the word as having "many resources." Line 21 of Book 1 also describes Odysseus as antitheos, whcih means "equal to the gods" or "godlike".
So, within the first 21 lines of Homer's epic, we have two significant indications that Odysseus has the skills necessary to overcome any obstacles in his path. He is a versatile person of many resources and he exhibits qualities comparable to the gods.
Thus, from the very first line of the poem, Homer gives us a major hint that Odysseus has what it takes to survive:
Tell me, Muse, of that man of many resources, who wandered far and wide, after sacking the holy citadel of Troy. (A.S. Kline translation)