Just to correct a misconception, the Aztecs (who were not a singular people but a confederation of Nahua peoples) are a North American group. Mexico is in North America.

That out of the way, there is an established record of trade from Central Mexico up through West Mexico into what is now NW Mexico/SW United States, with several intermediate polities flourishing during the Epiclassic and Early Post-Classic. We see this through evidence of southern goods, such as copper bells and macaw feathers, showing up in more northern areas, as well as cacao and rubber balls for ball courts. The full extent of this and whether it was direct trade or via intermediaries is still a matter of investigation and discussion, but there's very clear evidence that goods from Central/Southern Mexico were showing up among groups further to the North.

This was not "Aztec" trade though, it predates that political entity. By the Late Postclassic (i.e, Ye Olde Aztek Tymes) this trade complex had declined. In part this is because the groups further North declined in both terms of political integration and population, with an underlying factor that the entire region of southern and southwestern North America experienced increased aridity and drought which peaked in the 12th century CE. This same dry period acted as the "pump" for increased migration out of the increasingly drought stricken North-Central Mexico (Chichimecan) into the more fertile and hospitable lands of Central Mexico. Chief among these migrants were the Nahua groups which would settle in the Basin of Mexico, with the Mexica (who we most associate with the term "Aztec"), being relative latecomers in the late 13th/early 14th centuries.

The point of all this biogeography is that, at the same the people we now call Aztec were settling in Central Mexico, the trade routes further north were petering out. By the time of the Aztec imperial period in the early 15th Century, the clear signal of connection is absent. I'll defer to /u/ucumu and /u/mictlantecuhtli with regards to connections between the Aztecs and West Mexico, but I will note one particular barrier to Aztec merchants setting off to the northwest, the Tarascans. As the Aztecs expanded, the ended up butting up against another expanding Late Postclassic state, the Tarascans. After an expedition under Axayacatl in the 1470s was crushed, the two powers ended up settling into a stalemate of fortifications, spies, and skirmishes, which was still extant when the Spanish arrived. This, naturally, was not conducive to establishing long-distance relationships of trade or of anything else.

So why not move northward via an easterly route? The regions which are now northern Veracruz and Hidalgo had already fallen under Aztec dominance through expeditions against the Huaxtecs and Matlatzincos. The problem for this route was that the northeast gives way to arid lands more rapidly compared to the northwest, where the Sierra Madre Occidental extends up through the continent, creating the more hospitable climates of West Mexico before giving way to the Sonoran Desert. There was also no partner on the other end of the trade route like there was during the trade to the northwest in the Epiclassic/Early Postclassic. There are a few traces of connect, like an obsidian blade in Oklahoma and some scarce artifacts in Texas (obsidian points and ceramic sherds) with possible links back to Mexico, but definitive provenance and dating remains difficult.