I would recommend against pairing Battlemage with a low-spec CPU. As shown by Hardware Canucks, Hardware Unboxed, and others, Intel’s Arc graphics driver overhead is currently much higher than competitors, which means they’re disproportionately affected by having a weaker CPU. This causes the B580 to lose significantly more performance when paired with low-end CPUs than a roughly equivalent Nvidia or AMD card. At the very low end, the difference is especially stark. In some games, the B580 goes from neck-and-neck with a 4060 on a high-end CPU to losing half its performance with a low-end older CPU, while the 4060 only loses about 25%.

If you’re really stuck with a lower-end CPU, it would be far better to get a used midrange AMD or Nvidia GPU from an older product generation for the same price and use that.