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What you are describing in HVAC trade terms is an "economizer" setting. In many HVAC designs for larger (and some smaller) buildings when the outside air is cooler than inside air and the themostat calls for cooling, the controls will simply open dampers to simply exchange outside air for inside air. Often this happens in the evening.
Most residential systems use 100% recirculated air, but if you find a competent HVAC contractor willing to work with you a residential system could be configured.
Cheaply, you could tape a HEPA filter on a box fan, place it in a window and blank off the rest of the window. Just depends on how much ghetto you're willing to live with.
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