Did Dumbledore know that Harry would have to sacrifice himself from the very beginning?

Question

Based on the following interchange between Harry and Dumbledore in the pivotal "King's Cross" chapter of Deathly Hallows, I was wondering when exactly Dumbledore put together that Harry would have to die in order to bring about Voldemort's ultimate demise:

"And you knew this? You knew--all along?"

"I guessed. But my guesses have usually been good," said Dumbledore (Deathly Hallows, 599, hardcover).

The conversation that spurred Harry's question includes material dating back to Halloween '81, but also specifically mentions the events of the graveyard from GoF. So, "knowing all along" could refer to everything (i.e., Harry must die, Voldemort ignorantly tethered him to life, etc.) or just that Voldemort tethered him to life.

Other important information pertaining to this question can be found in OOTP, when Dumbledore confirms (if he didn't already know) that Harry contains part of Voldemort's soul. He uses the silver instrument to find out that Harry is just like Nagini, having the ability to share mind and soul with Voldemort. He also says the following:

"I guessed, nearly fifteen years ago," said Dumbledore, "when I saw the scar upon your forehead, what it might mean. I guessed that it might be the sign of a connection forged between you and Voldemort" (Order of the Phoenix, 826-827, hardcover).

While confirming that he guessed that Harry might share a connection with Voldemort from the very beginning, Dumbledore does not confirm with this statement that he knew Harry would ultimately have to give up his life.

In Philosopher's Stone, when Dumbledore drops off Harry on the Dursley's doorstep, we know he is not entirely truthful with McGonagall.

McGonagall asks: "How in the name of heaven did Harry survive?"

"We can only guess," said Dumbledore (Philosopher's Stone, 12, hardcover).

Of course, this was a lie. Dumbledore already knew how Harry survived, otherwise he wouldn't be delivering Harry to Lily's sister to extend the blood sacrifice. By proxy, he also knows that Voldemort will return b/c of Horcruxes, otherwise he wouldn't be so worried about Harry.

Finally, when asked in the same scene if he could remove the scar, Dumbledore says:

"Even if I could, I wouldn't. Scars can come in handy" (Philosopher's Stone, 15, hardcover).

So, did Dumbledore know at this very moment that Harry would have to die? Did he at least guess it to be true during this scene? We know he gains perfect confirmation in OOTP, but did he know it "all along," as a particular reading of the King's Cross interchange in DH would have us believe?

Answer 1

Clearly, Dumbledore knew that Harry would have to die as soon as he realized that Harry contained a piece of Voldemort's soul.

As to when he knew that, there are two options, both with valid arguments. My own opinion is that the second option is more correct:

OPTION 1: In OOTP, when he performed the "Essence divided" experiment

Rosi: What does "in essence divided" mean?
J.K. Rowling: Dumbledore suspected that the snake’s essence was divided – that it contained part of Voldemort’s soul, and that was why it was so very adept at doing his bidding.
J.K. Rowling: This also explained why Harry, the last and unintended Horcrux, could see so clearly through the snake’s eyes, just as he regularly sees through Voldemort’s.
J.K. Rowling: Dumbledore is thinking aloud here, edging towards the truth with the help of the Pensieve.
LEAKY CAULDRON - 7.20.07 - WEB CHAT TRANSCRIPT

(hat/tip @Slytherincess in this answer)

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OPTION 2: Basically, from birth.

This can be deduced from three quotes:

1. Deathly Hallows, "Prince's Tale":

   Another long silence. Then Snape said, “I thought . . . all those years . . . that we were protecting him for her. For Lily.”

   “We have protected him because it has been essential to teach him, to raise him, to let him try his strength,” said Dumbledore, his eyes still tight shut. “Meanwhile, the connection between them grows ever stronger, a parasitic growth. Sometimes I have thought he suspects it himself. If I know him, he will have arranged matters so that when he does set out to meet his death, it will truly mean the end of Voldemort.”

   Note that this "we have protected him" protection was arranged by Dumbledore from Harry's parents' death day, when he was left at Petunia's house.

   “You have kept him alive so that he can die at the right moment?”
   “Don’t be shocked, Severus. How many men and women have you watched die?”
   “Lately, only those whom I could not save,” said Snape. He stood up. “You have used me.”
   “Meaning?”
   “I have spied for you and lied for you, put myself in mortal danger for you. Everything was supposed to be to keep Lily Potter’s son safe. Now you tell me you have been raising him like a pig for slaughter—”

   ... at which point, Dumbledore doesn't deny it.

    ----
   

2. Another quote is actually one you have provided from OOTP:

   "I guessed, nearly fifteen years ago," said Dumbledore, "when I saw the scar upon your forehead, what it might mean. I guessed that it might be the sign of a connection forged between you and Voldemort"

    ----
   

3. And, lastly, we can deduce that Harry would have had to die from the following happening at the end of Goblet of Fire

   When Harry told of Wormtail piercing his arm with the dagger, however, Sirius let out a vehement exclamation and Dumbledore stood up so quickly that Harry started. Dumbledore walked around the desk and told Harry to stretch out his arm.
   Harry showed them both the place where his robes were torn and the cut beneath them.
   "He said my blood would make him stronger than if he'd used someone else's," Harry told Dumbledore. "He said the protection my - my mother left in me - he'd have it too. And he was right - he could touch me without hurting himself, he touched my face."
   For a fleeting instant, Harry thought he saw a gleam of something like triumph in Dumbledore's eyes. But next second. Harry was sure he had imagined it, for when Dumbledore had returned to his seat behind the desk, he looked as old and weary as Harry had ever seen him.

   Remember that Dumbledore wouldn't have cared about Voldemort taking in Harry's blood, except for ONE and ONLY one reason: that taking of blood is what would have tethered Harry to life, allowing him to survive being "killed" by Voldemort.

   As such, the only reason for Dumbledore to "triumph", never mind even care, about the event, would have been if he already knew that Harry would have had to sacrifice himself - and this simply gave him hope that Harry would be able to survive that sacrifice.