Latin mottos have been popular in Europe for centuries, but I have never seen anything comparable to a motto from the Roman era. When did first Latin mottos appear? (Examples of individual early mottos make nice partial answers, if you have such.)
The answer depends on what one means by a motto. For example, candida pro causa ense candido is a motto but senatus populusque Romanus is not. I like the definition given in Wikipedia: A motto (derived from the Latin muttum, 'mutter', by way of Italian motto, 'word', 'sentence') is a maxim, a phrase meant to formally summarize the general motivation or intention of an individual, family, social group or organization.
An insightful quote is not necessarily a motto. A phrase becomes a motto when some person or institution adopts it as their motto. To describe a motto well, one needs to give the motto itself and tell whose motto it is. My example motto above was from C. G. E. Mannerheim, but I resist the urge to go into Finnish history for details. I could rephrase the question: When did someone first take a Latin motto?
Note: I have accepted an answer. More answers are still welcome, and if someone has an earlier motto or a better explanation to offer, I am (as always) willing to accept a new answer.