Numbers may be older than letters.

With Sumerian cuneiform, some of the earliest examples appear to be inventories and maybe contracts and exchange records. For example this [1] appears to be a food ration token of some kind: Mouth bowl barley 4.

That's about 3100 BC or so. Five hundred years or so later, in developed cuneiform, those symbols still exist. By then they are usually abstracted into unrecognizable wedge shapes and lines. And by then they are definitely words, which had a reading aloud in Sumerian.

But back in 3100 BC, it's an open question whether they were thinking of the symbols that way.

There is an intermediate stage. One of the things you might want to account for is people. And their professions. [2] Again it is unclear if these are words. Eye city. (Guard?) King bull. (Chief herdsman?) What appears to be three tiers of gardener. Getting sophisticated. Within two centuries of that, we start to see the use of the pictograms to represent other values phonetically. A head is read as SAG. So if you want to write a name that has a syllable including SA or SAG you use the head symbol. And this is one of the key steps toward writing. But it is used sparingly at first. Names. Place names. Nouns for which there is no pictogram.

That is to say, more than 90% of the tablets continue to be beer receipts and the like. Around the same time, the kings and priests start to account and take inventory of their ancestors and battles as well. The language was probably Sumerian but there's almost no evidence of the Sumerian language itself in the writing yet. So few words written non-pictographically, no case markers or inflections or adpositions written yet. About 2600 BC the Sumerians start writing with grammatical markers, and the set of pictograms has developed into a system that can represent most of the sounds of Sumerian. And they start writing epic poetry and letters of complaint about their copper shipments being late.

I got a bit sidetracked sorry! My point is that the base-60 numerical system is fully developed at the earliest stage. It is used with the early pictograms.

Something similar may be true for the other meso- civilization in Mesoamerica. There's a fragment of an Olmec or Epi-Olmec stele with a date in the Long Count that, by Maya reckoning, would be in 36 BC. This is hundreds of years before the earliest examples of what is certainly writing, with the Maya. Things are very fragmentary so there is little certainty. But it seems possible Mesoamerican civilizations were recording absolute dates with their calendars, hundreds of years before they developed the ability to write arbitrary text.

[1] https://commons.wikimedia.org/wiki/File:Jemdet_Nasr_tablet_A...

[2] https://commons.wikimedia.org/wiki/File:Proto-cuneiform_Lu2_...