For a system being hit by a pirate raid, yes, I believe that pirate strength is intentional. Those are very low end barely into the cruiser tier pirate fleets. Since the game is a sandbox, there are going to be fleets you are not intended to defeat early game. You could take a commission with the Hegemony, and end up being hostile to Culann and Eochu Bres defense fleets on day 1 which are an order of magnitude or two harder than these fleets. You simply aren't expected to fight them.
I will point out there are 3 campaign quality of life skills that would make this much easier. Sensors would reduce your profile and increase your speed while running dark. Bulk Transport would boost your civilian burn speed to 9 (or even 10). Navigation would boost burn speed, but more importantly give Transverse Jump which just lets you leave the system from anywhere, not just jump points (although that can be earned elsewhere). These campaign layer skills can make the campaign layer much, much easier.
However, assuming no Navigation or Bulk Transport skills, no spare story points, and you don't feel your piloting skills and weapon availability are up to the task of taking one of these fleets out, I'd go to Ancrya and install the hullmods Augmented Drive Field, Militarized Subsystems, and Insulated Engines (or at least the ones you know), in that order of priority on your civillian ships. You can only fit 2 of them, but you may only know Militarized Subsystems. Then either restore (expensive), sell, or scrap any ships whose burn speed was still 8 or less. Presumably one of the salvage rigs with the burn speed reducing d-mod. Your fleet can and should be moving at burn speed 9, if not faster.
An early lesson you should take away from this as a new player is burn speed matters. If your fleet is burn speed 7, then the game while assume you've got capital class combat ships in it and fleets which contain ships weaker than capital ships will be able to catch you on the campaign map. If your fleet is burn speed 8, it assumes you have heavy combat cruisers in your fleet.
After you've gotten your fleets burn speed up to 9, you have a couple options:
1) Lure one or more fleets into a defensive battle with the station at Ancyra. Use sustained burn and emergency burn liberally. Help the station defeat them in detail. This assumes you are in good standing with the Hegemony.
2) Campaign layer sensor profile and position manipulation.
Step 1: While well away from Ancrya (so probably the far jump point), turn off your transponder, and move a decent distance away from the jump point, such that if you turn your transponder on, turn on sustained burn, and activate a sensor ping, all enemy fleets will see you, but far enough that you've got some time to react to when they do see you.
Step 2: Turn on transponder, turn on sustained burn, and ping.
Step 3: Immediately turn transponder off.
Step 4: Move perpendicular to the direction the fleets will be coming from. Sustained burn being on or off may need to be a judgement call and depends on how far out they can see you.
Step 5: After a short while, swing around and head to the jump point, and hopefully all the fleets will have passed you, and a sustained or emergency burn should beat them to the jump point even if they see you again. This is not that different from what you need to do for those stealthy missions to comm relays or that one question mission in Aztlan.
Edit: Ninja'd by others. Their advice is good.
