Here in North Texas where I live, mimosa trees are easy to grow from seeds. The seed pods fall from the trees and in that process may be blown for quite some distance by the wind. Wherever the seed pod lands, a mimosa tree is likely to sprout and start growing. I used to mow the tiny trees down along with the grass because I didn't want a forest, just the tree(s) I already had.
The new trees may not do as well in other parts of the country due to climate or soil. Contact your local county agriculture agent for free information specific to where you live for the best information on how to start a mimosa tree or trees from seeds and how to maintain them. Here where I live, they grow much like weeds, and so making sure they have enough water and trimming them occasionally like any other trees is about the only care they require.