Where did the Young Earth Creationist doctrine originate?

The Wikipedia article on Young Earth Creationism gives a good explanation of it's origins, decline, and revival.

Regarding the age of the earth, it cites Seder Olam Rabbah from 160 AD:

The earliest post-exilic Jewish chronicle preserved in the Hebrew language, the Seder Olam Rabbah compiled by Jose ben Halafta in 160 AD, dates the creation of the world to 3751 BC

The same article references the commentary on Genesis by Ibn Ezra (c. 1089–1164) for the view that the six days of creation were 24-hour periods.

Ibn Ezra believed in the Ptolemaic universe, common in the middle ages, that the Earth was in the center of the universe and didn't move. That it was encapsulated in nine concentric spheres embedded with the stars, planets, and other celestial bodies. The outer "diurnal" sphere revolved once every 24 hours.

With that background, we can understand Ibn's commentary on the creation as six 24 periods. For example, see his commentary on Genesis 1:5,8:

(5) by naming the light "day" and the darkness "night." The diurnal sphere revolved once, day blended into evening and night blended into dawn, day one.

(8) God named the heaven together with the air "sky." Although God had not completed God's work, the diurnal sphere revolved once, day blended into evening and night blended into dawn, a second day.

source: http://www.js.emory.edu/BLUMENTHAL/GenTradIbnEzraRamban.html

Philosophers at least as early as Philo (c. 20 BC – c. 50 AD) did not believe the earth was created in six literal days. Philo had this explanation:

II. (2) "And on the sixth day God finished his work which he had made." It would be a sign of great simplicity to think that the world was created in six days, or indeed at all in time; because all time is only the space of days and nights, and these things the motion of the sun as he passes over the earth and under the earth does necessarily make. But the sun is a portion of heaven, so that one must confess that time is a thing posterior to the world. Therefore it would be correctly said that the world was not created in time, but that time had its existence in consequence of the world. For it is the motion of the heaven that has displayed the nature of time.

(3) When, therefore, Moses says, "God completed his works on the sixth day," we must understand that he is speaking not of a number of days, but that he takes six as a perfect number.

See also Old Earth Creationism

If we go back to the earliest Christian teachers we will find a substantial focus on metaphorical and spiritual meanings of the Bible, more than maybe a modern Christian might expect. Roger Forster and Paul Marston write in "Reason and Faith" (Monarch, 1989):

In [the Church Fathers] there was, compared with today, a much greater emphasis on allegorical meaning of scripture. Thus, for example, Psalm 90:4 and 2 Peter 3:8 led many of them to take an allegorical interpretation of the 'days' in Genesis 1 to mean millenia. This view is expressed, for example, by Barnabas, Irenaeus, Hippolytus, Methodius, Lactantius, Theophilus and John of Damascus.

That was not the universal view:

Basil specifically refers to 24 hour periods, yet later writes: "Whether you call it a 'day' or whether you call it 'eternity', you express the same idea.

Chrysostom, who appears to take the 'days' literally in his homilies, repeatedly emphasises that ideas are being given 'concreteness of expression' in Genesis 1-3, to help our 'limited human understanding'. Thus on the 'rib' used to form Eve, he writes: "Don't take the words in human fashion; rather interpret the concreteness of the expressions from the viewpoint of human limitations. You see, if he had not used these words, how would we have been able to gain knowledge of these mysteries, which defy description".

Origen writes (around 231 AD):

What man of intelligence, I ask, will consider it a reasonable statement that the first and the second and the third day, in which there are said to be both morning and evening, existed without sun and moon and stars, while the first day was even without a heaven? And who could be found so silly as to believe that God, after the manner of a farmer, 'planted trees in a paradise East of Eden'? ... And ... when God is said to 'walk in the paradise in the evening, ... I do not think anyone will doubt that these are figurative expressions which indicate certain mysteries through semblance of history.

Augustine of Hippo writes:

Of what fashion these days were, it is either very hard or almost impossible to think, much more to speak. As for ordinary days, we see that they have no morning or evening but as the sun sets and rises. But the first three days had no sun, for that was made on the fourth day.

Augustine thought that the Genesis language reflected the Angelic perspective, which could know something either directly in God or in its later actual being.

The issue was not thought of as a crucial one to Christian belief.

The scientific evidence that pointed to an extremely old earth did not arise until the 18th century. This redating was not at the time generally taken as a 'disproof' of either Genesis or Christianity, and many of the scholars supporting it were Christian.

Significant Christian opposition to the geological dating did not arise until the early 20th century, with the Fundamentalism revival. Leading early exponents were George McReady price and Henry Morris. The Wikipedia article gives an excellent overview of the history.