The first occurrence of "Delphinum natare doces" I could find is in Erasmus' Adagia, after year 1500. Due to the nature of this book, the proverb itself must be much older than that.
Where and when does it originate from ?
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The Adagia of Erasmus was a compilation of Latin and Greek proverbs. This particular proverb (XCVII) is a translation from the Greek, as the entry makes clear. (I am using the 1703 Opera Omnia edition available on Google Books):
Δέλφῖνα νήχεσθαι διδάσκεις, id est Delphinum natare doces. In eos competit, qui monere quempiam conantur in ea re, in qua cum sit ipse exercitatissimus, nihil eget doctore. Nam delphinus in natando pernicissimi impetus est, ita vt non modo superet omne natatilium genus velocitate, verumetiam terrestrium animantium vt autor Aelianus libro xii. Quin et naues transilit seque contento spiritu teli in morem eiaculatur.
491 Δελφῖνα νήχεσθαι διδάσκεις Dieses Proverb findet sich bei den Paroemiographen: Zenob. 3, 30 = Ald. col. 67-68. Diogen. 4, 33. Suid. δελφῖνα 212 (cf. Adag. 393, n.l. 468). Diogen. 1, 65 (cf. Adag. 398, n.l. 498). Apost. 5, 96. Cf. Zenob. Ald. col. 68: Δελφῖνα νήχεσθαι παιδεύεις.
The very similar adage piscem natare doces (XIX) is explicitly attributed by Erasmus to Diogenianus (see the 1703 edition), so this strikes me as plausible.
Given that these Greek sources were compiled so long ago, I do not think it would be easy to trace the phrase further than this.