I fought against a much smaller force of precursors earlier and was successful. Granted, they had only 4 ships which fired salvos of about 30 AMMs at my fleet of about 10 ships (Ion to Magneto Plasma tech level). Since AMMs are only dealing 1 damage, a good way to deal with them are shields. All of my cruisers had a strength ~35 shield and 2 gauss turrets. The gauss turrets take a chunk of the salvo, the shields take the first salvo entirely and then regenerate until the next one and the rest was absorbed by 5-6 layers of armor. Whenever my ships got severely damaged (which mostly happened to my destroyers without shields), I moved them out of firing range. The aliens change targets at random so there is always some downtime where your shields can recharge.
Of course if you have salvos of 250 AMMs, you need a lot more shields and PD turrets to pull this strategy off, but it should work the same way.