Are all mammals capable of sneezing?
This national geographic post discusses many mammals that sneeze. It doesn't come right out and say all, but suggests most mammals have a cough and sneeze reflex:

Mammal coughs and sneezes come from throat and nasal passages, respectively, says Bill Milsom, a comparative physiologist at the University of British Columbia.
Mammals, he says, are the only animals that process food in the mouth by chewing. In other types of animals, like reptiles, &quot;food is swallowed whole or by chewing, and breathing is suspended during the event.&quot;

The same expert discusses non-mammals that sneeze, marine iguanas and fish.
You don't even need nerves or muscles to sneeze, per this Cell Press article

Sponges 'sneeze' without the benefit of nerves or muscles