There are two that are currently active. As a new commander you should seriously consider participating in the Caustic Heat Sink Launcher campaign. Why? Because in the Dumata system is buying Palladium for 200K/ton. Stations sell it for 50K/ton so you'll make 150K/ton profit.
Use the inara.cz commodity search tool to find nearby Outposts that still have . Why outposts? Because players with Fleet Carriers (like myself) will jump on any large pad station that has Palladium. But if you don't have a large ship yet small/medium pads work just as well. Note that even small pads within 60ly will be hard to find, so be prepared to do a few jumps.
Alternatively you could look for carrier loading/unloading jobs on r/EliteTraders/ or r/EliteCarriers where you'll get less per ton but will have a very quick turnaround so you can do several runs more quickly. Note that you won't receive trade rank for carrier load jobs, only for unloading jobs.
For about 3M credits you can have a that will haul 96t of cargo. You'll need another 5M credits to fill your hold. Completing one delivery will earn you 14M profit. Repeat that a few more times and you'll soon have the 70M you need for a that can carry 270t. Don't forget to upgrade the power plant, thrusters, and power distributor after completing a few more runs.
Disclaimer: I am a carrier owner and have posted a loading job for my fleet carrier.
