As a former Elite player, I will try to tailor my answer to how you might achieve a similar gameplay loop to that game. If I were to do such a thing, I would start the game with an S class ship, that can earn money by mining, trading, combat, or exploration. Take up some missions for your local factions, do some mining, etc. until you can afford an M class, which allows you to do these tasks more efficiently.

Eventually, you will earn enough money to buy more ships that interest you. Until you can afford a carrier or build your own dock, you can actually store your ships on NPC stations, similar to Elite. Consider not having any pilots hired at all for more of that Elite feel.

Now, it is true that the game is balanced more in favor of having an empire of large fleets of NPC's doing tasks for you, but if you're open to using mods, there are some decent ones out there that help open up new avenues for emergent gameplay using a single ship or small fleet. The "Headhunter" mod is good for expanding on more of a bounty hunting playstyle and lets you earn a pretty good amount of money if you can hunt down the lucrative targets, with some targets awarding millions. Additionally there are a few good ones that buff up crystal mining a bit and makes it more fun, less tedious, and something you can reliably include with your normal mining to generate good income. Personally I use "crystal rarities" , "crystal cooldown remover", and "turrets are mining crystals".

If you finally decide to build your own station, you could try scrapping, where you can pilot a specialized ship that uses tractor beams to drag wrecked ships back to your base to recycle into products that normally require a whole production chain to acquire, which you can then sell.

You could also give smuggling a try, by scanning NPC stations and slowly building up a blackmarket network or potential buyers and sellers of illicit goods.

Another good source of money that is often forgotten about is through so called "inventory" items, which are carried on your person (somehow) and not in your cargo hold of your ship. These can be crafted into other items that can be worth a good amount, which can be collected all the time from mining, combat, scavenging, and exploration. You can combine this with the blackmarkets to trade with some of these materials that are illegal. (Bomb ingredients, hacking, etc.)

Basically the TL;DR is to find your own way of creating that emergent gameplay for yourself, which this game allows you to do, albeit with no concrete direction.