This is the starter system and there are only basic ships there. You can mine quite well in a sidewinder, but it depends how much Cobalt the mission asks for. You can carry 9T in a Sidewinder if you fill up the refinery before leaving. Use a build like this:
A ship builder, outfitting and comparison tool for Elite Dangerous
coriolis.io
The problem is that by the time you've outfitted your ship, you could probably have made a lot more money doing something else, like bounty farming in the high resource extraction site in Dromi, which pays over 4 mil per hour. after a couple of hours there, you can get a T6 and do some serious mining for platinum (15 mil/hr) or Road to Riches planet scanning ( 10 -20 mil/hr) or Robigo passenger missions (60 mil hr).
Here's how to get those bounties without risk:
Source: https://www.youtube.com/watch?v=xdX-dZR3-aY