How much writing from ancient Greece is preserved? Is it a finite amount that someone could potentially read?

While there are 105 million words in the TLG, most of them are Byzantine. I did a count of the words in the corpus in Lerna VIc: A correction of word form counts in 2009; because there is not massive growth in the number of known ancient texts, the counts still apply.

If we define ancient Greece as up to the fourth century AD, and we exclude Christian works and technical works (so just literature, as opposed to writing), it’s 16 million words. If a novel is around 100,000 words, that corresponds to 160 books; so yes, someone could potentially read it. If we cut it down to strictly Ancient times (down to the fourth century BC), it’s 5 million words.

By way of comparison, the complete Loeb Classical Library (which includes all the important classical texts) has 337 volumes for Ancient Greek — and those aren’t 100,000 word-long door-stoppers.

How much has been discovered in recent years? Whatever we find in papyri, which has meant a few complete texts — notably Menander, and a trickle of new fragments like from Sappho (two in a decade). The occasional texts retrieved from manuscripts through improved technology, such as the Archimedes palimpsest. But it’s a trickle nowadays, and I would not expect it to ever become more than a trickle.