Prioritize replication. You can win with 1 in Speed and 1 in Exploration. Hazard Remediation should be 3 to 5 depending if you have the upgrades. And a 4 or 5 in Combat when you get it. Everything else should be put in Self-Replication.

You want to be over 10 Probe Trust when you start thinking about putting anything into Speed or Exploration.

Also, take one out of Hazard Remediation to put into any of the three Production skills as needed.

Once you see the percentage of universe explored start ticking up on the screen, the game is over. With a high enough Self-Replication, your growth is closer to exponential than linear. Doesn't matter if you're slow and don't explore far, you will just occupy the entire universe.