You should explore a first ...

You should explore a first flush system for your rainwater system.  These are normally sized to divert the first 1-2 mm of rain from the rainfall event into a separate tank before your main holding tank.  There are commercially available units or I have constructed them of pipe or 200 liter drums.   You should be able to find the information if you search for "first flush".  If you have a particularly heave load of dust, bird dropping you may need to oversize the first flush containers.  If you have several relatively small rainfalls you can collect more water if you install drain taps on your first flush.  This will save water and the water from the first flush maybe able to be used for floor mopping or such.  If you have relatively large rainfall events then you can install a small drain hole in the first flush container and the system will be automatic,

If needed then you can follow up with additional treatment as recommended previously.