So I've been thinking of ways that dude can out-wit the anti-magic field. It depends a lot on how the anti-magic field works, of course.
If magical effects simply cease to work once in the field, I don't see *any* way he could get around it. Since that's boring, I'll ignore it.
If new magical effects can't be started (via spells, enchantments, etc.) within the anti-magic field then there's some hope of either pre-planning everything to some absurd degree and having spell effects already in place to trigger or perhaps one could cast spells that cause spell effects from outside the range of the field which still affect things inside (launch a boulder from outside, it still falls down on the inside.)
One particularly effective way this could be addressed relatively simply is if the *upper* range of the anti-magic field isn't very high. If you could fly *over* the land and launch spell effects down *into* the country, it would be perfectly viable. Another, obvious, way to get around this sort of magic field is if you were to raise an army of undead or summon an army of fiends or whatnot from outside the field and march them into the field.
My *actual* guess though is he's going to pull the Isekai trick of bringing modern technology of some variety into the field of battle. Rolling into Daba in some form of Tank or delivering some kind of Daba-only nerve gas would be pretty lame but feels exactly like the sort of Isekai type resolution that would be used. Wouldn't surprise me if he's already though ahead and laced the bodies of their trophies with some kind of poison and is spreading it throughout. Then, of course, he gives the antidote to Lizard-Mc-Moe-Face and fucks her.
This whole series seems, so far, to enjoy playing Isekai straight long enough to throw it face first into the ground. "What sort of trick did you otherworlders bring to turn the tides?" "Nerve gas." "Ohshite"