We know each country has a starting land doctrine unlocked and presumably leveled up a bit at game start. How many levels does each country have in their starting doctrines? And do countries have default naval and air doctrines too?
You can switch trees at any time, but will loose the progress of the previous one and have to start at the beginning.
However, you do not necessarily start from scratch in your new Doctrine path: Several techs are shared between the paths, and if you switch to a path which includes a shared tech you have already researched you will start at that point in the new tree.