Try to ambush them? Design a ship with no weapons, but lots of engine, armor and one sensor and try to get them to jump into Sol, where you fleet will be waiting at the jump point and crush them while their sensors are down.
Could be a little risky; if you fail to stop them, you now have a lot of Precursors sitting in Sol. If you don't mind some game-breaking for the purpose of getting your game started, you could try some Rocks: huge commercial engines that light up the night, massive amounts of armor, and whatever CIWS you can pack on. Designed as civilian ships so they don't require maintenance, their sole purpose is to tank hits while your lighter ships go in and actually deliver the death-blow. The original design from blue emu's Ad Astra campaign:
Rock class Support Vessel 33,750 tons 556 Crew 1891 BP TCS 675 TH 2700 EM 0
4000 km/s Armour 10-93 Shields 0-0 Sensors 1/1/0/0 Damage Control Rating 1 PPV 0
Maint Capacity 35 MSP Max Repair 38 MSP
Ion Engine E0.8 (18) Power 150 Fuel Use 8% Signature 150 Armour 0 Exp 1%
Fuel Capacity 200,000 Litres Range 133.3 billion km (385 days at full power)
CIWS-120 (8x2) Range 1000 km TS: 12000 km/s ROF 5 Base 50% To Hit
This design is classed as a Commercial Vessel for maintenance purposes
The only catch is that it was created back before shock damage feature or the engine code redesign (in v5.42, to be precise); hard enough hits will hurt it even if they don't actually penetrate the armor. Due to their ridiculous effectiveness in that version against the AI, which isn't smart enough to identify it as not a threat and switch targets, I never used them myself, so I don't know how effective they'll be in new versions.
I've read the Ad Astra AAR, a damn good one I may add, and I'm considering using a version if this type of ship. But, that would take away space from my commercial shipyards that need to pump out freighters and asteroid miners, which I desperately need to avert a mineral crunch.
I'm thinking a large, conventional fleet, maybe 4 squadrons, which are 5 ships each. Grand parade around Earth and the Luna colony before they do battle, for "propaganda" and "restoring faith in the government" after the disaster at Alpha Centauri and the economic crisis. Because, I like adding some rp into my games. Makes it more exciting for me play.
Also, do asteroid miners store their own mined qminerals if they have their own cargo hold?