How is it possible that we will one day thank G-d for the exile?

Answer:

There is a promise in the book of Isaiah: "Observe justice and practice righteousness, for My salvation is soon to come and My charitable righteousness will soon be revealed."

In the time to come, the manner in which the exile is in fact an expression of divine righteousness will become apparent. At the present, it is a matter of faith. Since the sages teach us that "The Holy One, blessed be He, acted charitably towards His people by dispersing them amongst the nations of the world," we believe that this is so. This is not, however, comprehensible. For even after we have considered all the explanations offered for the exile (such as punishment for the people's sins, sifting scattered sparks of holiness, and so on), numerous ways are open to G-d; why, then, is there a need for the suffering of exile?

In future time, by contrast, in place of faith, everyone will palpably see how the exile was an expression of G-d's righteousness.

In this sense we can understand the prophetic verse, “On that day you will say, 'I shall thank You, G-d, for You were angry with me.'” This means that in future times, the good that lay hidden in the suffering of exile will be revealed; it will then be understood how this suffering enabled the Jewish people to be found worthy of the divine revelation of the time to come.

(From Exile to Redemption, 42-43. Isaiah 56:1, Pesachim 87b, Isaiah 12:1, Likutei Sichos vol. XX, p. 361, vol. IV, p. 1081)