It is not ancient history, but the Paston Letters would be a good candidate as the earliest example of a complete document set covering "ordinary people".

This is a surviving collection of around 1000 documents documenting the lives of a Norfolk family called the Pastons between 1422 and 1509. The documents include letters, wills, leases, inventories and even shopping lists.

The collection documents family business, but also personal matters: family fall-outs, parents nagging their children, parties thrown while parents were away from home, local gossip, requests for a replacement girdle to be purchased in London because one family member has grown so fat, commentary on the vagaries of the wool trade and complaints about the shortage of good servants.

This is a remarkable collection for three reasons:

First, as you note, it is unusual for such a set of documents to survive for anything other than the elite; the Pastons were gentry, the modern equivalent of middle class.

Second, they cover a truly fascinating period of English history, covering: the end of the Hundred Years War; the entirety of the Wars of the Roses; and the early Tudor period.

Third, one of the Pastons' chief correspondents (and their neighbour) was Sir John Fastolf, a professional soldier who fought prominently in the Hundred Years War and was one of the prototypes of Shakespeare's well known character John Falstaff.

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Sources:

British Library, which holds the letters now: https://blogs.bl.uk/digitisedmanuscripts/2015/04/the-paston-letters-go-live.html

Brittanica: https://www.britannica.com/topic/Paston-Letters

You might want to look into the Vindolanda Writing Tablets. (Online edition here: http://vindolanda.csad.ox.ac.uk/)

Vindolanda was a Roman Fort which had to be rebuild because ao high water levels. To raise ground, a lot of material was leveled on the site and then sealed off with a package of clay. The finds became waterlogged and lots of items survived that are rare in archaeological context. Some of the writing tablets contain parts of private letters. I remember one of a soldier thanking a relative for warm socks, so there are glimpses from everyday life of normal people accessible.

You're right on with ancient Roman graffiti - it's one of the most democratic forms of self-expression that survives from antiquity. A solid source on these will give you great examples of the types of graffiti that survive, where they were found, what they mean, etc. One I particularly like is Alison E. and MGCL Cooley's Pompeii and Herculaneum: A Sourcebook (Routledge; second edition 2014),^(1) which shows graffiti from various time periods (i.e. not all from AD 79) and then broken into thematic categories like leisure, religion, politics, etc.

Also, look for sourcebooks on antiquity. These will include snippets of literature as they relate to various categories - the military, women, certain historical events, etc - so you can get a sense of the different kinds of information about daily life that's buried in lengthy texts you might otherwise not pick up when looking just for information about the ancient everyman. There are a lot of them out there on different topics, time periods, etc, that will likely satisfy and pique your curiosity further!

^(1) There are two editions of this with two names, which is a bit confusing at first. The authors are the same, but the first edition - 2004 - is only on Pompeii (Pompeii: A Sourcebook, Routledge). I prefer the second edition since it includes Herculaneum and thus provides a more complete picture of life in this area, but the first edition has documents from the 19th century excavations at Pompeii, and the second edition drops these.