A box fan in a room will usually give you more air changes than typical HVAC

For me, it just doesn’t remove the particulates fast enough when they’re quite dense outside or the house is porous.

Better sealed homes might have better luck - it should work ok - but the best way to breathe filtered air quickly is to stick your head right above a filter.

You can drop a boxfan-filter combo anywhere, even where there's no forced-air HVAC.