Is it possible for a small country to have a very large gdp without being export driven?

Luxembourg, It has a really good tourist industry among the Rich and affluent, so it has a high GDP. It can't do much exports because it is land locked.

GDP is determined not only by productivity but by the number of workers and so a country that has a small population can never have a large GDP only a large GDP per capita. Small rich countries must import for much of what they consume so must also have a large export sector  to pay for their imports. Germany has a large export sector because they are part if the EU and  has an economy that is inter meshed with the rest of Europe and most of their exports are to other EU nations. Trade accounts for olly a little more of the GDP in Japan than it does for the US.