Probably not a lot. The Pantheon as we see it today was built under the Emperor Hadrian (with restorations by Septimius Severus early in the 3rd century and many small changes since), on the site of the original Pantheon built by Agrippa between 27 and 25 BC (his name is still on the front of the building). Agrippa's temple was struck by lightning and totally destroyed - Hadrian's version was apparently a complete rebuilding. Before Agrippa's construction, this part of Rome was an open area known as the Campus Martius, reserved for military exercises and political assemblies, so the original temple was built on empty ground.

There have been some excavations in and aroud the Pantheon, but very limited. The building was converted into a church in the early 7th century and has remained an active place of worship ever since. That, combined with its obvious attraction for tourists, has made investigating the building very difficult without causing major disruption, not to mention potential damage to one of the best-preserved Roman buildings anywhere in the world. Late-19th century excavations in the portico and inside the church confirmed the existence of a pre-Hadrianic structure underneath the current building, including a podium and paved floor. A more recent dig (1996-7) at the front of the temple revealed that both the Agrippan and Hadrianic buildings had staircases leading up to their podiums.

Further reading:

Platner and Ashby (1929) A Topographical Dictionary of Ancient Rome (Entry for the Pantheon online here)

La Rocca, Eugenio. “Agrippa’s Pantheon and Its Origin.” The Pantheon: From Antiquity to the Present, edited by Tod A. Marder and Mark Wilson Jones, Cambridge University Press, Cambridge, 2015, pp. 49–78. (Online here but behind paywall)