Imagine Civilization, but in space, and maybe crossed with the Foundation series by Asimov. It's really really good, and the new patch (2.0) makes it much more enjoyable (in true Civil fashion, where you wait for the mature DLC or big balancing summer patch to really bring the game into its stride).
Have you encountered that problem and/or do you know if it has been addressed?
If you do encounter that in a game just do what you'd perhaps do 'in real life': try and be friends with them and not tempt them to anihalate you until you're strong enough to defend yourself. That might mean giving them resources, or not taking stars near their borders. And obviously up your ship building capacity and start investing more resources there.
But Stellaris fails to pull it off. There are a few sleeping giants which, after learning the hard way, you'll just ignore until you are ready to take them on. When you have mastered those pitfalls (and that isn't hard) you are back to the single-minded race for empire, with no interesting goals for those left behind due to some early blunder which stalled the resource throughput growth rate for a while.
Stellaris is trying to be generic (the Stellaris world could be the background for almost any interstellar epic, it's full of little cameo references to every sci-fi classic the authors could think of), where Alpha Centauri went to great lengths filling the canvas, in one specific way.