Question:

If all the great sages, mystics, and holy people of the past generations were unable to bring Moshiach in their lifetimes, how can we imagine we will be able to make it happen?

Response:

The thing to realize about redemption is that it is not an all-or-nothing proposition. Bringing Moshiach is not the sole responsibility of any one generation; it is the culmination of a collective effort, goodness accumulated throughout the ages. And goodness doesn't disappear.

Also, there is a specific benefit to being in this generation.The Chassidic masters teach that the purpose of creation is to make this world into a dwelling place for G‑d. Not the worlds of the angels, not some heavenly realm of souls and spiritual beings—but this earthy, palpable, mundane physical world. In order to bring Moshiach, this is what we need to work on—we've got to bring G‑d down to earth.

Let me ask you: Is there any generation that better qualifies as being "down on earth” than ours? For Moshiach to come, the G‑dly needs to be revealed in us. In what the Kabbalists call "the lower realms." In fact, the generation before the coming of Moshiach is called the "heel of Moshiach" because the world is at its lowest point since Sinai.

When I was younger, I used to sew needlepoint tapestries. One of the first ones I ever sewed was a picture of a quaint cottage, surrounded with trees and colorful flowers, with a bright blue sky and puffy white, gray, and dark gray clouds. While sewing it, I decided that the grays of the clouds were too dreary. So I replaced them with bright blue and white. When I finished the picture it didn't look quite right. Those darker, "drearier" colors were necessary to make the picture perfect. Sure, the vital reds and pinks and yellows and bright greens "made" the picture—but without the simple grays, the somber browns, and the unobtrusive blacks, the picture was not complete.

Each and every one of us has a crucial role in drawing the divine picture and bringing Moshiach; if you didn't, you would not have been created. Telling ourselves that we have no power, are insignificant, unimportant, and don't matter is simply a product of laziness. On the contrary, the very fact that we are such ordinary people, struggling with the most earthly, mundane matters—that's exactly what qualifies us more than any other generation to bring G‑d down to earth. You can't invite Him in unless you live there yourself!

Remember, G‑d put us in this position because He believes in us. And if He does, so should we.

Sources
This concept of G‑d wanting to dwell in the "lower realms" is so central that we have an entire section devoted to this subject on our site. The source most often cited for this concept is Tanya, chapter 37. However, there he cites the Midrash of Rabbi Tanchuma.