Much precontact art served as mnemonic devices, most notably wampum belts, in which the color (purple or white) of the shell beads, designs, and numbers of beads all had meanings, which specialized belt readers could comprehend.

Pottery designs, petroglyphs, birchbark scrolls, quillwork, etc. all conveyed complex information to those familiar with their iconography. Carved wooden calendar sticks were used both by the Great Lakes and Colorado River tribes to record important information.

Songs and dances also are ways for communities to record specialized information. For example the Caddo Turkey Dance begins a cycle of dances that describes Caddo emergence, migrations, and warfare. The songs are sung in the different languages of the tribes that make up the Caddo confederacy.

In the Mojave and Sonoran deserts songs, such as the Paiute Salt Songs establish a cadence for long distance runners and the songs coincide with the landscape and provide valuable information about water sources, etc.

One of many reasons that elders are highly respected in Native American societies is their extensive knowledge of oral history and medicine. In a preliterate society, memory is revered.

Just as an aside, you know that in Mesoamerica more than just the Maya had a writing system? There was Epi-Olmec, Zapotec, Teotihuacano, and Mexica that I know of. Granted Teotihuacano and Mexica were most likely used as pneumatic devices for recalling things memorized.

North of the Rio Grande I know that the Mi'kmaq and Algonquin both had writing systems, as well.

The question assumes that the answer will be the same for all Indigenous peoples living in North America - the fact is, there will be no one consistent answer that will accurately reflect the historical realities of all groups, because these communities are so diverse. (Not to slam the OP, I just want to make explicit something that they might have assumed everyone would know.)

That said, I think ahalenia has outlined some great points. I'd affirm what she said and emphasize that this is really just scraping the surface of what constitutes Indigenous information transcription.

It's also important to note that just because they weren't alphabetical doesn't mean that some Indigenous ways of transcribing information should not be called "writing systems." For example, if we consider Egyptian hieroglyphs to be a "writing system" why do we not also consider symbols woven onto baskets, painted on rock, or carved into poles to also be "writing systems"? Some of it, I think, is because these traces can be harder to find (baskets and totem poles disintegrate more quickly than stone carvings), and some of it is, imo, also the legacy of colonialism. When explorers and settlers encountered Indigenous peoples, it was easier for the former to dismiss the latter as savages and thus justify colonialism and "civilization" if they didn't have things like a written language. And, certainly, these alternate forms of information transcription were not readily apparent to Europeans as forms of writing, so their response is understandable. But that has meant that today, there is an assumption that Indigenous peoples did not have written language, and this is something that is contested by some of those communities today. I have read and heard of elders in the community I work with (in British Columbia) reject the idea that they did not have a written language, pointing to things like weaving and memory sticks as documents which, sure, look different from words on paper, but which are still valid examples of forms of information transcription.