The first time I ran the career missions, I found no need to belt mine in system. I got some of the stuff requested by looting my wrecks, some only required tritanium and I had lots of that from missions, the cap boosters needed pyerite and mexallon - can’t mine that in the new player systems anyway so I had to go to a 0.7 system to find plagioclase. I got the frigate as a reward for one of the exploration missions. I watched YouTube walkthroughs which made it a lot easier but, I’m still here 5 years later so something clicked!
Those who want to mine anyway can find Asteroid Belt Remnants in their anomaly scanner. These were created long before the NPC fleets showed up because the normal belts in starter systems tended to be mined out anyway - gankers aren’t allowed to operate there.