Triads (i.e., three notes comprising "modern-day triads") existed before the 16th century, but they were not understood as "triads". The use of triads becomes more prominent around that time, however, and the theory of triads is believed to have arisen about a century later.
Three notes sounding harmoniously together goes back well before the 16th century. The composer(s) who first put three notes together is unknowable.
But as an example of "triads" occurring in music before the 16th century, here is an excerpt from Guillaume de Machaut's Messe de Nostre Dame, "Kyrie", written sometime before 1365.
SOURCE IMSLP, edited by Thomas Milligan
On beat 5, we can find a E minor triad, moving to a C major triad on beat 6. However, these would not have been understood as "triads" in the sense that we use the term.
By the 16th century, the use of triads becomes more prominent, and more clearly headed in the direction of how we think of them now.
Josquin Desprez's "El Grillo" (1505):
SOURCE: IMSLP, edited by Pierre Gouin
Analytically, we have several major and one minor triad, but they still would not have been thought of that way at the time.
F | G Dm | C (open 5th) | (open 5th) D | (open 5th) | C |
From the (Western) music theory perspective, the idea of a "triad" — that three notes form a specific harmonic unit — is generally attributed to Johannes Lippius, in the 17th century. For example:
The reception of Johannes Lippius’s path-breaking conception of the triad chiefly relies upon his  treatise Synopsis musicae novae. (SOURCE)
The term "harmonic triad" was coined by Johannes Lippius in his Synopsis musicae novae (1612). [SOURCE: Wikipedia: Triad (music)]
Jean-Phillippe Rameau is generally credited with first articulating the modern conception of a triad and its musical function in his 1722 Traité de l'harmonie réduite à ses principes naturels (Treatise on Harmony).