I'm surprised nobody's mentioned it yet, but there's a fairly easy way to edit the initial ship(s) you start with.
Go into starfarer-core/data/world/factions/player, open it with your standard text editor.
You'll see a 'fleet compositions' section, with 'start1', 'start2', and 'start3'. I'm not sure what start1 is, to be honest. Start2 is what you start with, and start3 is what you'll end up in if you bet the house and lose.
maxFleetPoints does what it says on the tin. If you set it to 0 (which is the default), you'll get one ship at random.
The crew, supplies, marines and fuel seem to be based on whatever capacity you start with. So 30-40 days worth for a single ship will be numerically much less than a full fleet.
The ships portion has variant names followed by two numbers in brackets. Take the variant names from starfarer-core/data/variants; if you know what you want pick it, otherwise feel free to experiment. First number in brackets is the minimum number you can start with, second is the max-- but you won't go over the fleet point limit. If it crashes on startup then you probably typed something in wrong, but if I recall previous versions had one or two variants in the variant file that don't work.
One thing you'll notice is that there are a bunch of 'starting' variants commented out (the #). I don't think there's any other way to get those, so feel free to experiment. They tend to not be great, but starting with a fleet of starter frigates is interesting.
Finally, not sure how to add fighters. Maybe follow the 'wing' format in start1?
Note that a mod might have its own 'player' faction file that will override this.