While getting down to the exact day would require some newspaper work, reference to the general highway maps, particularly the official state issued ones, would be good enough for a year by year work.
Also, at least in my state, every time a route opens there is a "Commissioner's Order" that declares it a public road, describes its end points, and assigns it its number. An example for an interstate might be: "The Commissioner (legalese) declares a new route, to be designated as Interstate 64, to be a public road and to run from a junction with I-64 previously designated at MM 15 at Ona in Cabell County to MM 39 and junction with State Route 34 at Teays in Putnam County.
These are recorded in a vault at the Capitol just like a county deed record room. While not computerized, they are indexed and fairly easily searchable.
I would love to see such a set of maps.