At least two of the pirate factions (Guristas and Archangels) are a breeze to get standings for. They both have their own special L3 Epic Arc.
Both of those give you 30% base Faction Standings, which is a MASSIVE amount by any standard, and which unlike other faction standings do NOT concomitantly increase/decrease other faction standings! Get Social V and those standings turn into 37.5%, which along with Diplomacy I will get you from -10.0 to just over -2.0 so you can access L2-4 agents.
Both arcs take an evening to complete, each, and can be completed in frigates. I use a sub-2s rage rocket malediction myself. Also, both arcs can be started from Empire agents, so you don’t need to have good Guristas or Archangel standings to gain access to these arcs.
Lastly, the arcs grant you something like 25% corp standings, which helps push you up to being able to access L3 missions right off the bat. Oh, and each Arc mission counts as an L3 mission for unlocking a Storyline mission of the same level, so after the arc you just need to run 4-6 more L3 missions to reach the 16/16 requirement to unlock a storyline, which you can then complete for HUGE amounts of Corp standings to get you even closer to, or above, 5.0 corp so you can access L4 missions.
Don’t even joke about running L1 missions. They are CCP’s ultimate punishment for those who have damned their standings.