Max out ground build slots +1
Max out space build slots +1 (Primary Defence Station, Secondary Defence Station, Construction Station (Shipyard, Ship Market, Pirate Base) and Economic Station (Golan Colony, Trade Port))

You also start at 5, not 4. If you build the government building you'll have 6.

So start with 5, +1 from gov building, +2 from infrastructure, and +2 from filling all ground and space slots will give you 10 influence.