Based on Game of Life: Kill the Sun
Conditions are the same:
Below is an initial state for Conway's Game of Life with a single pulsar. Living cells are white.
The area marked with red is your base. You are free to modify any of the red cells, but only those, and only in the initial generation. You are not allowed to do anything once the simulation starts.
Your goal is to move the pulsar so that its center is within area of the base – in other words, the game must reach a generation where only a pulsar with its center in the red area remains/loops infinitely and everything else is destroyed. Yet in other, way cooler words:
You have to construct a rocket to move the Sun and nothing else that was created in the process to remain.
The grid is infinite in every direction, i. e. runaway gliders still count as living.
EDIT: Because all answers are correct and there is no easy way to choose which one is the most valid, I'm picking the one with the most votes. I hope this will not discourage others to post other interesting solutions.