When was the diameter of Titan first measured? Titan is enshrouded in a thick opaque cloud of methane : with a telescope, you can't see the moon's surface. Because of this, from a distance, you can only see the diameter of the moon + its atmosphere, not the diameter of the moon itself.
When was the diameter of Titan first measured and how?
Discovery of Titan, 1655: Unknown diameter.
Dollfus, 1970: 4,850$\pm$300km (1). Measured by Filar micrometer (2) and diskmeter / double-image micrometer (3).  (Apparently a summary of earlier measurements, currently trying to find print copy)
NASA SP-340, 1974: Summary of above techniques, propose settling on 5,000km diameter until it can be measured by stellar occultation (the same process used to determine the size and shape of Ultima Thule). (4)
Elliot, 1975: Measured the diameter by limb darkening / lunar occultation (i.e. by how Titan passed by Saturn).
Calculated diameter somewhere between 5,132$\pm$47km and 5,832$\pm$53km.  (5)
Pioneer 11, 1979: Only 5,800km found in references, appears to still be using the 1975 calculation. (6)
Voyager 1, 1980: Same as above.
Cassini, 2004: The Cassini probe had radar which was able to &quot;see&quot; right through Titan's atmosphere.  Although the first flyby was on July 2, 2004, it appears that the radar was not used until the second of the 45 planned flybys (7,8).
This paper from 2009 combined data from all of Cassini's passes at that point.  This allowed the authors to build a model of the actual surface over enough of Titan to determine its size (~5150km) and that it is slightly oblate, like the Earth.  In terms of actually measuring the surface, this is probably the best answer.
(1): Surfaces and interiors of planets and satellites, Dollfus, Audouin, 1970.  Page 129 is apparently the specific table.
(2): Lunar Occultation of Saturn. I. The Diameters of Tethys, Dione, Rhea, Titan, and lapetus, Elliot, J.L., 1975.