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There is a trick that allows you to do this actually. While the basic zone infiltration/ventilation objects do not work in an AFN model, HVAC does.

What you can do then, if you want to model the baseline fresh air/infiltration rate simply like this, is to instead deliver it through your HVAC system. Use DesignSpecification:OutdoorAir to specify your desired infiltration rate (which can itself be scheduled), and then apply that to e.g. a basic Ideal Loads system. Make sure the System Availability Schedule is always on (so the system can always provide air), and if you want to schedule the heating/cooling use the Heating Availability Schedule and Cooling Availability Schedule inputs.

Note that this obviously does have limitations - the air provided here will not interact with the AFN and affect the pressures throughout the airflow network at all. It is just adding a certain amount of fresh air completely separate to whatever air is being provided from window opening. That being said, in most situations where there is significant natural ventilation through the windows for cooling it would likely overpower the infiltration anyway. And given how uncertain any natural ventilation estimates are (both in terms of the ventilation modelling and the assumed occupant behaviour) worrying about details like that probably isn't worth it.

Example use:

 DesignSpecification:OutdoorAir,
    infrate,                 !- Name
    AirChanges/Hour,         !- Outdoor Air Method
    0,                 !- Outdoor Air Flow per Person {m3/s-person}
    0,                       !- Outdoor Air Flow per Zone Floor Area {m3/s-m2}
    0,                       !- Outdoor Air Flow per Zone {m3/s}
    0.35,                    !- Outdoor Air Flow Air Changes per Hour {1/hr}
    Always On;               !- Outdoor Air Schedule Name

HVACTemplate:Zone:IdealLoadsAirSystem,
    Masterbedroom1,          !- Zone Name
    ,                        !- Template Thermostat Name
    Always On,               !- System Availability Schedule Name
    50,                      !- Maximum Heating Supply Air Temperature {C}
    13,                      !- Minimum Cooling Supply Air Temperature {C}
    0.0156,                  !- Maximum Heating Supply Air Humidity Ratio {kgWater/kgDryAir}
    0.0077,                  !- Minimum Cooling Supply Air Humidity Ratio {kgWater/kgDryAir}
    NoLimit,                 !- Heating Limit
    ,                        !- Maximum Heating Air Flow Rate {m3/s}
    ,                        !- Maximum Sensible Heating Capacity {W}
    NoLimit,                 !- Cooling Limit
    ,                        !- Maximum Cooling Air Flow Rate {m3/s}
    ,                        !- Maximum Total Cooling Capacity {W}
    HVAC_day,               !- Heating Availability Schedule Name
    HVAC_day,               !- Cooling Availability Schedule Name
    None,                    !- Dehumidification Control Type
    0.7,                     !- Cooling Sensible Heat Ratio {dimensionless}
    60,                      !- Dehumidification Setpoint {percent}
    None,                    !- Humidification Control Type
    30,                      !- Humidification Setpoint {percent}
    DetailedSpecification,   !- Outdoor Air Method
    0.00944,                 !- Outdoor Air Flow Rate per Person {m3/s}
    0,                       !- Outdoor Air Flow Rate per Zone Floor Area {m3/s-m2}
    0,                       !- Outdoor Air Flow Rate per Zone {m3/s}
    infrate,                 !- Design Specification Outdoor Air Object Name
    None;                    !- Demand Controlled Ventilation Type