The Miami (Myaamia) people did not "come to" Indiana—they are indigenous to it.
Their historic homeland (Myaamionki) centered on the Wabash River valley in present-day Indiana and western Ohio. Key villages included Kekionga (near Fort Wayne) and Pickawillany (near Piqua, OH).
They were part of the Algonquian-speaking Great Lakes confederacies. Forced removals (1840s) sent many to Kansas, then Oklahoma (where the Miami Tribe of Oklahoma is now based). The Miami Nation of Indiana (non-federally recognized) remains in the homeland.
So: they didn't arrive; they were already there when Europeans entered the region.