What determines civilian growth beyond that? The number of colonies.
, how busy it is transporting stuff and presumably getting paid, the number of civilian mines, or perhaps all of these?
A civilian line will build a new ship when
a) there is an immediate shipping need (available freight for export matching import need elsewhere, or available population at "Source" colony matching unfilled pop capacity at "Destination" colony) that is large enough to fill a new ship and that does not have a civ ship already assigned
and b) the civilian line has enough money to build a new ship.
By creating and growing new colonies, you naturally create the need for civilian shipping capacity.
If you want them to grow faster, you can make lots of transport contracts. For example, make contracts to move 1000 infrastructure to Luna, then when it is done, make contracts to move it all back to Earth. You pay the lines for each shipment they make, so this is essentially a way to subsidize them.