Making contact with the Grox isn't particularly easy in itself - they are at the centre of the galaxy which will most likely be a long trek from any colony you've established, and even further from your homeworld. Upon completion of all the other missions your homeworld has to offer you, and upon reaching a sufficiently high empire rank, you will be given the mission to make contact with the Grox, and eventually to investigate the Galactic Core which the Grox seem to be protecting.