This is, of course, a matter of personal opinion. My own view is that the US was justified if you look at things from the perspective of Americans in the 1800s. However, if you look at things from a modern point of view, westward expansion was not justified.
When you look at things using today’s ideas of morality and justice, the US was in no way justified in expanding westward. The lands in the West were occupied. They belonged to the Native Americans and to Mexico. You could argue that the Spaniards of Mexico did not deserve their land because they had taken it from the natives of their country, but you cannot really make a similar argument about the Native Americans. By today’s morality, you cannot simply go and take another country’s land just because you have the power to do so. Therefore, there is no way that westward expansion was justified.
By contemporary standards, though, westward expansion was justified. In those days, countries routinely fought one another for territory. In those days, people still believed in racial superiority and that some cultures were simply better than others. From this point of view, westward expansion was justified. Americans were superior to the Indians and the Mexicans in terms of their culture and their race (this is the idea of Manifest Destiny). In addition, might made right and America was justified in taking land if it had the power to do so.
These are two different views held at two different times. Which one makes more sense to you?