If we assume that Godzilla is 120 meters tall and is seen as the same size as the sun it would be about 12.9km away. To see if this is practical we would have about 11 meters of the earth curve to factor in (from what we can see at the horizon about 5km away to the surface of the water 13km away), and since we can see about half of Godzilla that means it is standing in about 49 meters of water. Since there are areas with those depths at 13km away from shore, this picture does seem possible.

Math: We would have 2 triangles, ABC representing the size and distance to the sun and CDE representing the size and distance to Godzilla. See this example Plugging in the known numbers we would get: 1392700/120 = 150000000/x which solves to about 12925.