Is it permissible to emigrate to a Western country to obtain a passport, with the intention of returning to the Islamic world later, knowing that this might require residing there for three years?

Traveling to and residing in non-Muslim lands and acquiring their citizenship is not permissible except out of necessity and to the extent of that necessity, or for a recognized need, provided the Muslim is confident in his steadfastness in his religion and character. If you are compelled to obtain this citizenship, then there is no harm in traveling to and residing among them until you achieve your objective.