Asymmetric 4X, the player starts in the middle surrounded by various aliens the goal being conquest of the galaxy (50% let's say) and survival against late game invasion of aliens from another galaxy spawning around the edges of the galaxy. Purely singleplayer game.

I have implemented most of the things, the player starts with 50 planets in the middle, AI attack, etc. Everything is fine except the game flow. If I made the AI too strong it crushes the player, if I made it too weak the player conquers everyone without effort, if I made them balanced... there is a stalemate :D

So, it's kind of "overbalanced" I need somehow to make it so the game can progress (player can win but with effort).

I'm not sure how to make it... The AI produces a static number of units per turn (partially based on number of planets), the player can produce units highly depending on population size (planets are needed to house population) so the player's production capabilities grow over time, with a soft cap (bureaucracy eat up most of the income after reaching 20 billion population), also the payer has research.

Somehow, I need to make it so the player can upset the balance. Or change the flow of the game? I don't know...

If the player is better than alien, they win, else they lose.

You can add random events and hidden knowledge to create opportunities to change the tide of battle, if that fits the game. So if alien is winning, maybe player can strike a weakness to prevent defeat.

That would make the "uncertainty" region of who will win, bigger, since theres more unknowns. So game remains interesting for longer, when its not just the first moments of gameplay that determine the winner.

Then, the problem of momentum. Once a side is winning, what prevents them from pushing through all the way?

First, just make everything slow enough, so it takes some time. Maybe taking over a planet is not instantaneous, maybe you need to build infrastructure before being able to push further.

Second, let the battlefront oscillate. Like a spring with ever increasing energy, until it finally exceeds a limit in either end and one side is victorious. You push hard, both sides lose resources, but you are left with weakened force, allowing alien to push back, repeat.

One way to implement that would be to give limited offensive power to both sides, that takes time to regenerate, and isnt sufficient to wipe out the entire enemy in one go. Basically, you 'spend' your offensive capability to hurt the enemy somewhere, but have to go defensive after that, giving enemy an opportunity to do the same.

If the player is better than alien, they win, else they lose.

Typically, in 4X, everyone starts with 1 planet. The AI gets early bonuses so instantly becomes stronger than the player. The player lie low in that phase. Then, since the player is smarter eventually there comes a point when sides are equal (mid game). After a while the player becomes stronger and starts extermination of the AI (late game).

In my case it works different. You basicly start at the mid game (a lot of fleets guarding planets, 10-50 planets under your control, most planets in the galaxy already colonized). So, it start in a quite balanced state... which is not best for the gameflow :)

Once a side is winning, what prevents them from pushing through all the way?

One way to implement that would be to give limited offensive power to both sides, that takes time to regenerate, and isnt sufficient to wipe out the entire enemy in one go. Basically, you 'spend' your offensive capability to hurt the enemy somewhere, but have to go defensive after that, giving enemy an opportunity to do the same.

I have the problem with the stalemate.

This is where I would start on a 4x game, before all the little details about population and food, or what weapons the ships would have. Everything else should be built to serve whatever you come up with to give the game good flow.

When I play civilization on an easy setting, I get to a point where I can tell that I'm far in the lead and that I'm going to win, but still have several hours of game play until I win. This can ruin the state of flow for me even more than a stalemate. A game that allows bigger swings in battle can help with this for both the winning and losing players. If you're winning, you could take advantage of your lead to defeat your opponent quickly, while a losing player could take a risk to quickly even the playing field. This might make it more challenging to achieve a balance so a player that wins one war doesn't move on to take over the whole world/galaxy every time, but I think has more potential for an exciting game. When you do have a well balanced war, instead of feeling bored by the stale mate, you would be excited to know that either player can tip the war in their favor at any moment.

Also, in civilization a stalemate in wars can still work because there are other victory conditions that you'll eventually get to after you've researched the end game tech. An end condition like the space race allows players to always be making progress towards something, instead of simply gaining and losing ground.

So, to trivialize the suggestion: the player has a "rage bar" when it fills up the player can fire it up and all ships get +100% damage for 30 turns :) AND/OR AI has -50% damage for 20 turns then +50% to damage for 20 turns and the cycle repeats? :)