The fear that lunar dust was fine, deep, and motile enough that a lander could sink under its surface was mostly backed by Thomas Gold, a noted astrophysicist who was a consultant to NASA in the 1950s.
Note especially in the image below of a Popular Mechanics article from 1964, the quote from his article in Science magazine on the subject:
"Without any clear signs [in Ranger images]
of firm rock, the pictures must lead to more concern about sinkage of impact."
He became in the small minority in this thinking over time and isolated in his position, but he stuck to his guns. There were some at the time who felt no more needed to be known about the lunar surface before attention could turn to sending people.
Note that this makes him the first person to recognize that the surface of the Moon has been primarily shaped by impacts. The entire surface of the Moon is covered with dust that is tens of meters deep (mixed with larger particles) entirely produced by meteor impacts pulverizing it and throwing it around over billions of years. (You don't sink in it, but it's there.) This understanding led to the realization that all solar system bodies experienced high levels of collisions for large parts of its history, and research later established that the Late Heavy Bombardment occurred, and that impacts were a major mechanism of the solar system's evolution. In turn, this realization probably influenced the development of the theory that the Moon was in fact created by an impact event between early Earth and an object about the size of Mars.
The first Surveyor mission was thus in large part meant to determine whether the dust on the surface would support a spacecraft. From Wikipedia on the Surveyor program:
Several Surveyor spacecraft had robotic shovels designed to test lunar
soil mechanics. Before the Soviet Luna 9 mission (landing four months
before Surveyor 1) and the Surveyor project, it was unknown how deep
the dust on the Moon was. If the dust was too deep, then no astronaut
could land. The Surveyor program proved that landings were possible.