Trust between Nations comes in three steps:
- Mutual interests / Mutual damages
Mutual interest / damages
During point 1, since we are in the weaker position, it's up to us, to find something the aliens want, and to make it easier to get it through us, instead of just wiping us out (e.g. selling them iron at a loss, or providing a buffer zone between them and an enemy of theirs). Should we have nothing material to offer them, we must appeal to whatever value system the aliens have ("It's a pity we don't have your spaceship technology, we were planing to build a big temple to Zumpflargel on mars.").
Should that also not be an option, we need to try to make it inconvenient to not be allied with us. This would be a tighrope walk, since we'd need to provide enough of a disincentive to be bothersome, but not enough to warrant a military intervention (which we would assumedly loose).
The same as step 1, but turned up to 11. We now need to become so good at whatever worked in step 1, that all alien alternatives become second rate compared to what we offer. The goal is to make it so, that the aliens can't wipe us out without loosing a valuable asset. If we have reached this step, we can start bargaining with the aliens on a more even footing.
Alternatively, we play technological catchup and hope we can reach mutually assured destruction before the aliens notice.
This is the best possible outcome. Earth and the aliens have existed together for so long, that social and political boundaries become weak. A good unifying identity is needed for this step - a idea of "us"ness that can be appreciated by both the aliens and earth.
Hopefully such common ground can be found through natural social processes, because so far there has been little luck in RL to engineer this.
The good part about the steps above is, that they don't need trust - they are just based arround self-interest.