YouTuber Macsen Lets Plays makes great content for single-player 4X games on high difficulties. His commentary is insightful, and his diligence with adding YouTube annotations to clarify or correct is seriously impressive. Here I've pulled out some important points from his Stellaris opening guide, especially ones that parallel ideas of strategy in other games.
Macsen starts off pointing out the importance of quick starts in 4x games:
The best early game government types are in Macsen's opinion despotic empire and plutocratic oligarchy, for reducing construction costs and increasing minerals income:
Increasing minerals income early is a key part of a rapid Stellaris start:
So make sure to use your starting minerals to create mines that increase mineral income:
To get a good position out of the opening, expand quickly, and to expand quickly, research Colony Ship immediately. Keep an eye on the research time and minerals income. Try to have the 350 minerals needed for a colony ship stored up so that the moment research completes construction begins:
Split up the initial fleet to explore more quickly, and without risking the loss of multiple ships at once:
Meeting a new type of alien grants the player a society research project to learn more. In the early game, these society projects are noob traps, because they incur the opportunity cost of pausing ongoing society technology research (in this case, Colony Ship tech) for the duration of the project:
Preemptively weaken your neighbors, so they can be more cost-effectively added to your empire later. Identify their preferred planet type and zone them out of suitable colonization targets with your own outpost and colony placement.
Races starting with the xenophobic trait are better equipped than most to jump start their games by conquering primitive civilizations, adding their planets and population to the empire without the expensive wait for a colony to build up. Conquering primitives gives a relationship malus with all other met empires, so here Macsen temporarily stops exploration so he can conquer the natives before meeting AI empires.
In the early game, freely giving research agreements to AI players is a cost-effective way to get a significant relationship bonus at very low cost. Since the player has only a few relatively cheap techs in the early game, the AI will not gain much extra science from the agreement.