Rush the shipyard, first colony ship, and space elevator in the first few turns. Personally I don't rush the starport and use the cash for other reasons but others might. Tile placement to use adjacency bonuses also helps a lot.

It’s important to customise ship designs, you don’t need to build colony and construction ships with huge ranges to colonise a planet which isn’t far away. Keep the designs simple, just the colony/construction module and some variants with different numbers of range modules. This way you can build ships massively faster and cheaper.

Have you first ideology pick as pragmatic (for 3 construction ships) and then focus on malevolent motivation which provides absolutely massive production bonuses. To be honest this part of ideology is still way OP and needs to be nerfed. Frankly, if I was Brad, I would code every AI to do this given how much better it is than any other choice at the moment.

Your initial citizens as administrators are essential to enable that expansion.

A custom race can be very powerful. Be warned some traits seem to be bugged (e.g. colonisers don't give first free improvement as stated).

If you have the mercenaries expansion a long range scanning ship can be very useful to quickly map out the area to send colony/construction ships safely to key locations before the AI. An extra survey ship or two can be useful to accelerate gains from anomalies.

The benefits of improved strategy are huge.  On my current game on Genius (played more Godlike than anything else prior to Crusade but dropped it down while I tinker with the new mechanics) I have about double the nearest AI’s number of colonies and starbases after the initial expansion phase.

Also - if the game is using a "Faction" as versus a CIV and you have not edited (giving it proper attributes) it looks like the game defaults giving it:

• Colonyship
• Scanner ship
• Constructor

They can immediately populate 1 planet, create a shipyard and start scanning the anomalies. 

I started trying to convert my factions over to Civs (Ulons - which you are showing above), but when I save them they do not show up under Civs, so it's still saving them as a Faction, so not sure if they are being saved properly. With so many other bugs I highly doubt it.

I agree with a lot of what Icemaniaa says.

I do a few things slightly different but a lot of the principles are the same.  You definitely want to have a plan and to leverage everything you can think of since the AI expansion is no joke.

I rush a starport and another survey ship to use for scouting (find the best worlds to colonize faster) and to grab more anomolies (tend to get cash and research boosts).  You can rush partially constructed stuff.

Some barebones designs for colony/const are a must and drastically reduce build times.  I use a colony ship that's just a hull with the colony module for "short range" colonizing that takes about half the time to build as the default colony ship.

I only ever play as a custom race (with some portraits and graphics added via nexus) - we're able to build a civ that suits us perfectly, so why not.

I can do one better, 10 turns in, Normal difficulty. The AI has two planets and took a 3rd in 3 more turns.  My first reaction was that the AI cheated like hell but when I was able to get Universal Translator and look at their civilization I did note they had a colony ship right off the bat.   But the AI was 'lucky' to get three inhabitable worlds so close as I had set habitable planets to Uncommon.

Another thing of note is the starbases and constructors it already has.  Turn 10??? Right..... And when I did communicate with the empire, around 4 turns later, it still had 2500 credits.  So for those of you saying it rush built, how?  Where'd it get the credits to rush build 2 colonist ships, a shipyard, and 3 or more constructors, all in 10 turns???

Still, if it's legit, the AI did expand correctly.  I just don't see how it was possible playing fair.

I read here or on discord that the ai was getting free ship rush which is fixed by patch