Life and industry create waste. But life and industry may reuse waste. Recycling is likely to be central to a martian economy, as the cost of new goods will always be high, in particular goods that need to be transported from Earth. Recycling facilities for complex technological items may have to wait, but atmospheric and water recycling will be required from day one.
Waste biomass recycling is likely to start on the ships to Mars. Or at least the waste from the ships occupants will be recycled on Mars, like any other resource.