This is a question with much debate and theories. To resolve the answer, we must first look at events that have more trustful dates. There are 3 events that provide a more consensus date;
- Year of Aram and Israel joined forces to attack Jerusalem, 735BC
- Year of the fallen of Israel to Assyria, 722BC
- Year of Sennacherib besiege Jerusalem, 701BC
Let's first start with Isaiah 7:14, the sign of Messiah "Therefore the Lord himself will give you a sign: The virgin will conceive and give birth to a son, and will call him Immanuel"
This sign if only applied to Jesus 730 years later, has no implication to Ahaz at that time. Isaiah used the word "almah", which translated to "virgin", instead of the formal Hebrew word "bethulah", which has a specific reason. "almah" refers to a woman of childbearing age, but has not been married. Moreover, it has a deeper meaning of "hidden, concealed" that supposedly hasn't been met by the boys. So Isaiah prophecies to Ahaz, "I know you have a secret lover, and now she is pregnant, and she will give birth to a boy, not a girl, and God will be with him." It might have shocked Ahaz that Isaiah knew, and more likely he knew she was pregnant before Ahaz realized, and he knew it was a boy, the next King Hezekiah.
Now we look at 2 Kings 18:13 "In the fourteenth year of King Hezekiah’s reign, Sennacherib king of Assyria attacked all the fortified cities of Judah and captured them." Count backward from 701BC, Hezekiah became King in 715BC, not in compliance to 728BC (3rd year of Hoshea in 2 Kings 18:1); and by the time he was 20, not in compliance to 25 (in 2 Kings 18:2).
If the above is valid, Ahaz became King in 731BC at 20, so Isaiah met him in 735BC while he was 16. This seems to fulfill he had a young secret lover. 2 Kings 15:32 told the father of Ahaz, Jotham reigned in Jerusalem for 16 years, 2 Kings 15:30 told in the 20th year of Jotham, Hoshea assassinated Pekah and took the Israel Kingship, that we know it was 730BC.
As a devote Christian, I totally understand the stake in taking this hypothesis. However, even if I accepted the original verses completely, the verses themselves did not add up to a logical sense.
- 2 Kings 15:30; Hoshea took the Israel Kingship (730BC) in the 20th year of Jotham. Let's say Jotham reigned in 749BC for 16 years, Ahaz reigned in 734BC at 20; Hezekiah reigned in 728BC (2 Kings 18:1-2) at 25, that made Ahaz had Hezekiah as a son when he was one year old!
- If Ahaz coregent with Jotham, Ahaz died at 36 when Hezekiah was 25, made Ahaz have Hezekiah as a son when he was 11, oops!
- If Ahaz was coregent with Jotham, Ahaz started reigned in 743BC, by the time Pekah was in his 7th year, not in compliance to 2 Kings 16:1-2, 17th year.
- If Hezekiah reigned in 728BC (2 Kings 18:1), his 14th year is 715BC, by the time the Assyrian King was Sargon II (722-705BC), not Sennacherib (2 Kings 18:13)
There is an intense struggle should we take every single word in the Bible infallible as it had been warned in Revelation 22:18-19, or there is a greater will of God that through a time of frequent hand coping and translations, who is capable to devote his life to know him.
May God give us wisdom in reading his book.
By the way, 2 Kings 18:7 says "And the Lord was with him (Hezekiah)...."
Recommend reference from Journal Article "The Date of Hezekiah's Birth" by John McHugh posted in JSTOR.