Did Moses write YHWH or God's full name?

My Hebrew instructors have informed me that the language had not developed to the point of using four letters for God's name in the time of Moses. That came in about the time of David. Around David's time, the scribes began adding the final "ה/heh". It was not used as a consonant, but as one of the early vowel markers, popularly called "matres lectionis," Latin for "reading mothers" because they help the reader know how to pronounce the word.

Conventional wisdom says that the Hebrew alphabet was preceded by, and descended from, the Phoenician alphabet. However, some scholars have concluded that it may have been the other way around, and that Moses played a principal part in the invention of the Hebrew alphabet. The earliest books of the Bible were written by Moses, who had been educated in Pharaoh's court.

Few would question, however, that at the time of Moses the alphabet consisted only of consonants, which did not include the final "heh" in the Tetragrammaton. Like the "w" in English, which functions as both a consonant and a vowel in "willow", the "heh" in Hebrew can be either consonant or vowel.

Scholars differ on whether the scribes who were copying Moses' books later, such as in the time of David, may have used the updated spellings which had developed by then. Of special interest is one passage in Exodus where the "heh," thought to have been added to God's name by those scribes, may turn one of God's statements into exactly the opposite if understood, instead, as a consonant--the "interrogative 'he'" prefix to the following word (word spaces were not then in use either).

Consider:

And I appeared unto Abraham, unto Isaac, and unto Jacob, by the name of God Almighty, but by my name JEHOVAH was I not known to them. (Exodus 6:3, KJV)

וָאֵרָ֗א אֶל־אַבְרָהָ֛ם אֶל־יִצְחָ֥ק וְאֶֽל־יַעֲקֹ֖ב בְּאֵ֣ל שַׁדָּ֑י וּשְׁמִ֣י יְהוָ֔ה לֹ֥א נֹודַ֖עְתִּי לָהֶֽם׃ (TR)

Placing the "ה/heh" on the following word means that it becomes a question rather than a statement--the "ה" being used as a grammatical marker to indicate the start of a question. Considered in this way, the translation might be:

[RETRANSLATED]

And I appeared unto Abraham, unto Isaac, and unto Jacob, by the name of God Almighty, and by my name JEHOVAH, was I not known to them? (Exodus 6:3)

(Note that the "and" in this Hebrew text is usually translated as "and" but is sometimes acceptably translated as "but" or as "now.")

Rendered in this fashion, verse 3 appears consistent with the statements made immediately following. It also removes a contradiction from the Bible in that the Bible is clear that Abraham knew God's name.

And Abraham called the name of that place Jehovah-jireh: as it is said to this day, In the mount of the LORD it shall be seen. (Genesis 22:14, KJV)

(Even the word "the LORD" is "Yahweh" in the Hebrew.)

Exodus 6:3 stands as evidence that in the time of Moses, God's name would have been written with three letters, YHW, instead of the four which it came to be later.

Conclusion

Based on the evidence we have today, Moses would not have written the full four-character "Tetragrammaton" of God's name: he would have written only the three consonantal letters. The fourth letter, added later as a "matres lectionis" vowel, would have been a usage unknown in Moses' time.

UPDATE (I re-read the question and caught its pronunciation emphasis!):

Because none of the Hebrew words were written with vowels in Moses' day, the pronunciations for all of them would have been rooted in oral tradition. The earliest written vowels began to creep into the language in about the time of David and the First Temple Period. That one of these was specifically added to God's name shows that they were indeed teaching its pronunciation, and were not ashamed to speak it.

Around 300 BC is when God's name was declared ineffable, and its pronunciation nearly ceased. For a time, the high priest would say that name once a year, on the Day of Atonement. Eventually, the original pronunciation of the name would be entirely forgotten and it is now lost to history. We can guess, perhaps accurately, perhaps not, at what it may have been; but no one now living can know with certainty.