I think making it so your enemy AI can't attack early is primordial. You want the player to have a certain level of understanding of your gameplay mechanics before threats come up.
As a colloquial to the above, while enemies may have very deep empires, you may have it so that no ships are already constructed, so they'll spend at least a few turns building up an army. Then, if lucky enough, they'll duke it out on their own.
In a 2d map setting (fairly illogical but standard to most 4X games), you may choose to have the player start nearby a corner so that he can't be surrounded early on. This decreases the statistical chance of being attacked early assuming most erratic AIs will attack somewhere near and the player will share edges with fewer empires as a result.
Also, you need to have something that grants the defender's advantage: that way, despite being in smaller numbers, the player is able to hold his ground for a bit. Arguably, it is best if he can start conquering fast.
Think: how does one single planet starts to rule them all?
You could have it so that a single faction occupies most of the territory around the player, and that this faction is at war with most of the other species. This would simulate the "ashes of an empire", where the player is really just rebelling from an empire that is crumbling down. As the game progresses, you'd see a weakening empire around you leaving fewer and fewer defenses, giving you a chance to quickly claim valuable planets without much resistance. This should allow you to ramp-up to a mid-sized empire fairly quickly after just a few turns (10-20 or 30 maybe?)
Then, you'd come face-to-face with the other factions and the player would find himself confined to whatever he was able to grab, and improve his defenses.
The cool part here is that it would shift the flow back and forth and that different games would net different outcomes:
- Capture too many planets in the first expansion phase and you'll have trouble setting up appropriate defenses vs all players, and your empire may find itself shrinking rapidly.
- Capture too few planets in the first expansion phase and you'll have trouble setting up an economy that allows you to build said defenses
*This would teach the player more about your economy and they would learn through trial and error and direct feedback 20-30 turns into the game.