The sugars need to dissolve in order to get the texture just right.
Anyone that came to their store that day got free scoops of ice cream. Until the 18th century, ice cream mostly consisted of dairy-free flavored ices cream. Accept the way things are in life. You will need to make it using the freshest and strongest coffee beans you can and straight from your coffee machine.
You might also consider buying battery-operated novelty ice cream makers for those backyard barbecues.