An assembly is provided for a turbine engine. This assembly includes a swirler and a fuel nozzle. The swirler is configured with an outer wall, an inner wall, an outer passage and an inner passage. The outer wall circumscribes the inner wall and extends axially along an axis to a distal outer wall end. The inner wall extends axially along the axis to a distal inner wall end that is axially recessed within the swirler from the distal outer wall end. The outer passage is formed by and radially between the inner wall and the outer wall. The inner passage is formed by and radially within the inner wall. The fuel nozzle projects into the inner passage. The fuel nozzle is configured with a plurality of orifices axially aligned with the inner wall and arranged circumferentially about the axis.