King Ahaz is the subject in Isaiah 7:14. If you read chapter 7 and 8. The prophecy was fulfilled 700 years before Jesus.
It is clear from the narrative in this chapter, that Isaiah’s declaration (Is 7:14-16) was a prophecy about the unsuccessful siege of Jerusalem by the two armies from the north. The verses Isaiah 7:15-16 state that, by the time this child (whose imminent birth was foretold in Isaiah 7:14) reaches the age of maturity (“… he knows to reject bad and choose good …”), the kings of the two enemy nations will be gone, in fact, they will be killed. Two Biblical passages, 2 Kings 15:29-30 and 2 Kings 16:9, confirm that this prophecy was contemporaneously fulfilled when these two kings were assassinated. With an understanding of the context of Isaiah 7:14 alone, it is evident that the name of the child in Isaiah 7:14, Immanu'el, is a sign which points to the divine protection that King Ahaz and his people would enjoy from their otherwise certain demise at the hands of these two enemies. Clearly, Isaiah 7:14 is a near-term prophecy that is part of an historic narrative, and which was fulfilled in the immediate time frame, not some seven-and-a-half centuries in the future.
So who is the subject of Isaiah 9:6?