According to Opacity of an Ionized Gas, "light from regions [of the sun] where the pressure is greater than 0.01 atm. is cut off completely, so that all we see comes from a spherical shell of rarefied gas".
There is no real surface of the Sun. Instead, the density and pressure of gas/plasma progressively increase from an infinitesimal value far from the Sun, to a very high value in the core of the Sun. If you flew at a level where the pressure is similar to atmospheric pressure of the Earth, you could not see anything (except light emitted from your immediate vicinity), according the the above statement.
See table 2-1 of The Photosphere for quantitative information on the opacity of the sun at different height. Only at a height in the sun's atmosphere where density is ~$1/10000$ of Earth's at sea level is a photon more likely than not to have a free path out of the sun without being scatterred or absorbed.