Corn appears to have been bred about 7000BC, and spread south: Ecuador 6000BC ± N lower Central America 5600BC, Columbian Andes 4500BC ± N -- New Mexico and Arizona about 2500BC, and to reach beyond the desert took more than 2500 more years.
Seeds are easy to pack, and if you keep them dry they ought to keep a long while. But the "how to grow" them might be a little less portable, if traders weren't usually farmers.
Transfer of knowledge and plants is trivial if the farmers migrate or intermarry along the routes, straightforward if trading travel is part-time or everybody learns a bit of everything, and hard if trading is a specialization, or if the people you trade with aren't really into agriculture on a large scale.
I wonder what the barriers were that slowed corn reaching far into North America. Desert would be one, obviously. Were the deserts and jungles of those eras in the same places as now? I've done a little searching, and so far haven't found systematic climate studies that cover enough of the area to game out which way people might go. If somebody knows, I'm curious. Up and down the coast should be pretty straightforward.
Remote areas having nothing you cared to cart back is another barrier, as are hostiles. Great Lakes copper went east, south to Georgia, north to Alaska--but I don't see references to the SouthWest. Well after Great Lakes copper started being used, South American started smelting their own--and possibly that was easier to get than stuff from the north. But one map on that page shows marine shells being traded across the deserts, so trade wasn't impossible.
Of course, the trade routes may have developed later than the movement of corn growing, which happened pretty early in most places.
I got started down a rabbit hole trying to figure out how trade worked from the Pacific to the Amazon side of the Andes. Incas traded for feathers and skins, and even tried to invade--how old were the trade routes? Would they have been possible for the Caral-Supe, circa 3500BC, 3000 to 4700 years earlier?