Rocket engine Wikipedia article states that
Goddard was the first to use a De Laval nozzle on a solid-propellant (gunpowder) rocket engine, doubling the thrust and increasing the efficiency by a factor of about twenty-five. This was the birth of the modern rocket engine.
This source elaborates a bit more on this:
In 1915, as assistant professor at Clark University, Worcester, he [Robert Goddard] began experiments on the efficiency of rockets. He bought some commercial rockets and measured their thrust using a ballistic pendulum, a heavy mass suspended by ropes, to which the rocket was attached. The rocket was fired, and the height to which the pendulum rose provided a measure of the total momentum (mass times velocity) imparted to it.
Goddard experimented on his ballistic pendulum with various nozzle designs, using a small metal combustion chamber filled with a type of gunpowder, ignited by electricity. The end of the chamber was threaded, so that nozzles of various designs could be screwed onto it and tested. Using a De Laval nozzle, he obtained jet velocities between 7000 and 8000 ft/sec and efficiencies of up to 63%. Later he replaced the ballistic pendulum with a more compact device, in which the thrust of the rockets did not lift a pendulum against gravity but compressed a calibrated spring. With that device he showed that (contrary to some popular claims) rockets worked just as well in a vacuum.
De Laval's nozzle turned spaceflight from a vague dream into a real possibility. Goddard communicated his results to the Smithsonian Institution in Washington and asked for support to develop a rocket capable of probing the high atmosphere. ... In January 1917 the Smithsonian responded with a grant of $5000, and Goddard began his rocketry career.
The above describes what we would call nowadays a static fire test.
Then the storyline omits further details of the solid rocket development and continues with liquid fueled rocket:
The idea of feeding the rocket with a continuous stream of solid charges also proved unfeasible, and in 1922 Goddard went back to his alternative idea, proposed independently by Hermann Oberth in Germany and also noted by Tsiolkovsky: a liquid-fuel rocket
So, between 1915 and 1922, did Goddard build a solid fueled rocket with de Laval nozzle that actually was trialled in a real flight? If not, was it his (first ever) liquid fueled rocket "Nell", that was flight tested on March 16, 1926, to be the first flying rocket to utilise de Laval nozzle?
Sketches of the rockets from 1914 Goddard patents that show de Laval nozzles (source)