The professional way to clean jewellery is to use an ultrasonic bath. The vibration releases the dirt particles from the smallest recesses of the jewellery.
To do this as a hack you need to replicate the vibration as best you can.
Place the jewellery in a small dish and cover it with water in which you add a small amount of washing up liquid.
This now needs to be vibrated. Good sources of vibration about the house would include a washing machine on a spin cycle or a loudspeaker. Obviously you need to take care that no spillage of the liquid can occur and the dish doesn't slide off onto the floor.
Leave the dish to vibrate for 15-20 minutes and rinse off the jewellery.
This should remove much of the dirt. No scrubbing or brushing has taken place. This works for any metal, not just silver.