Exactly how do you find this? The Wiki says it will show up/Appear after your first warp. Which I did at the start of the game after fixing my ship, and spending about 3 hours harvesting runes for a few million. Do you have to go through the base building to get this started or can you do it without building a base at all?

The Anomaly will appear very early in the Artemis quest. Answer the communicator calls.

You may need to build a minimal base. If I recall correctly, the prompts push you to build a "four walls and a roof" base along with a blueprint research station to complement the base computer. I don't know if that is a prerequisite to trigger the Artemis quest, though.

Yes, I needed to build the base and do the few quests after for the event to trigger.