We built the ships and the linear accelerator in orbit around Jupiter. After all, all the fuel you’ll ever need is right there, and you don’t have to go far for metals.
We would finish two ships, fling one, flip the accelerator around to face the other direction, and fling the next; that way, the recoil is cancelled. Twenty-eight colony ships were launched that way, before the war.
Now, with Earth in the first years of a nuclear winter that may last a millennium, we’re on our own up here. At least we got some eggs out of the basket.