Are your white trainers 'fright'trainers? Have you forgotten what they looked like in their new pristine whiteness?
Try mixing some baking soda with white vinegar. Mix it up to a paste. Grab an old toothbrush and plaster the mixture over all white surfaces - not suitable for colours. Give the shoes a good scrub with the mixture and if possible, leave to dry in the sun. Once dry, brush, or wash off the mixture and put your sunglasses on!