Hi,
I will start with a disclaimer: I don't intend to brag, I just want to shortly explain how I played to beat the game on godlike, albeit with some settings that helped me out. The game can for sure get harder. Also any tricks or things I haven't thought of are welcome.
Settings: Custom civ, Synthethic, starfaring, and all bonuses that help with production and efficient ships. 3 planet start.
11 alien civs, tiny spiral map. rare star and planet frequency. No resources, abundant anomalies.
Game pace and research very slow. Abundant events, disabled tech trading and surrendering.
The general idea is to build tall asap with the 3 planets you have, priority is to take the lead in tech. It will take a while before you have catched up, so stay peaceful until you are comfortable with taking out the swarms of ships in your space belonging to some civ that will likely attack you sooner or later.
I start off buying a cheap colony ship (design built with only the colony module), and buy improvements in your capital city, about 3 manufacturing and the rest research. Then let them grow to max pop size. As soon as you have an event for ideology points, get 3 free constructors and upgrade all 3 to constructors with 2 modules. Then build a ring of 5 economic starbases around your capital. For module number 6 I would recommend a military or cultural starbase in an expected combat zone/border.
Tech wise it is important to get freighters out quickly and get far enough up in diplomacy you can get free trade agreements, boosting your income. With that income rush buy improvements and pop. Once you have enough morale it's time to maximize pop by getting the right pop techs. When your 3 planets have around 25-30 pop you should be in the tech lead; from here you can start military techs to get some ships. Getting a few fast transports are good to have stocked, in case you can take profit from 2 neighbours fighting; you could then almost take the planets for free. Whenever the pressure is off, for example when you have signed non aggression agreements with most neighbours try to grow your planets. Eventually I won like this, with almost all techs discovered. There were some huge fights with 4000hp fleets attacking eachother.
What I don't like is you need to carpet space with starbases and keep them all upgraded. On a small map its ok to handle. But I have done an insane map once, and gave up after I had 40 planets and over 200 starbases. Also I find the AI not that good. Biggest annoyance is that sometimes the game crashes to desktop when I eject a ship from a starbase.