It would appear that the Septuagint may be the first translation of the ancient Hebrew scriptures to have retained YHWH. Although retaining the Hebrew form of this word is not a transliteration, please bear with me as I explain what happened.
In the time of Ptolomaic rule over Judea (320 to 198 B.C.) many Greek people came in to Judea, their culture influencing the people. This hellenization resulted in a Greek translation of the Hebrew scriptures. It began to be written around 285 B.C. and was finished during the 100s B.C. The Septuagint became the scriptures for Greek speaking Jews of the first century A.D. and the apostle Paul used it when quoting from the Hebrew scriptures, though he never kept the Hebrew YHWH, but wrote Greek for ‘Lord’. This is significant when Paul quoted Hebrew text referring to Yahweh but applied it to Jesus Christ. This was a transliteration. Was it the earliest, the first?
From this link below the claim is made that,
“In the earliest manuscripts of the Septuagint the Tetragrammaton was
given in Hebrew letters, which in Greek circles were supposed to be
Greek and were read πιπι (Field, "Origenis Hexaplorum Quæ Supersunt,"
i. 90, Oxford, 1875; Herzog-Hauck, l.c. viii. 530; Blau, l.c. p.
131).”
http://www.jewishencyclopedia.com/articles/14346-tetragrammaton
I have no knowledge of whether those earliest manuscripts of the Septuagint were actually Greek and were read πιπι, or not. However, if they were, then that would be a transliteration.
According to the link below, there are ancient Greek manuscripts, such as the Septuagint, proto-masoretic, kaige, translation by Aquila of Sinope, Symmachus the Ebionite, Theodotion and the Hexapla [written by Origen in the first half of the third century A.D.] that contain the Hebrew YHWH or that have it in paleo-Hebrew script. Those would not be transliterations.
However, it is important to note that that particular manuscript fragment in the entry below is a REVISION of the Septuagint, so that the Septuagint original will pre-date it.
It adds that there is a book on this written by Emanuel Tov in 1990: Discoveries in the Judean Desert: VIII. The Greek Minor Prophets Scroll from Nahal Hever (8HevXIIgr). Oxford: Clarendon Press. ISBN 978-0-198263272
https://en.wikipedia.org/wiki/Greek_Minor_Prophets_Scroll_from_Nahal_Hever
Now, your question asks about earliest transliterations of the Hebrew Tetragrammaton, yet I have written about retaining the Hebrew, not transliterations of it (apart from the possibility of a transliteration into Greek in the link http://www.jewishencyclopedia.com/articles/14346-tetragrammaton
This is where my final link is of significance.
The Septuagint represents the first major effort at translating a
significant religious text from one language into another. It is
interesting to note that many of the New Testament quotes from the
Hebrew Bible are taken from the Septuagint. As faithful as the
Septuagint translators strived to be in accurately rendering the
Hebrew text into Greek, some translational differences arose. In
comparing the New Testament quotations of the Hebrew Bible, it is
clear that the Septuagint was often used. This is the result of the
fact that by the late 1st century B.C., and especially the 1st century
A.D. – the Septuagint had “replaced” the Hebrew Bible as the
Scriptures most people used. Since most people spoke and read Greek as
their primary language, and the Greek authorities strongly encouraged
the use of Greek, the Septuagint became much more common than the
Hebrew Old Testament. The fact that the Apostles and New Testament
authors felt comfortable, under the direction of the Holy Spirit, in
using the Septuagint should give us assurance that a translation of
the original languages of the Bible is still the authoritative Word of
God.
http://www.gotquestion.org/YHWH.html
Please note how the apostle Paul transliterated his quotations from the Hebrew scriptures where the Tetragrammaton occurred, into the Greek word for ‘Lord’.
Obviously, if another answer gives evidence of the Tetragrammaton being transliterated in manuscripts predating Paul’s writings (all completed before A.D. 70), then my answer will need to be corrected.
