Do Abraham and Isaac symbolize God and Christ?

Short Answer: Church father such as Origen, Athanasius, Luther, and Augustine would certainly say so. I would agree with them.

There are definitely some key parallels:

The sacrifice of the son:

• Isaac: Abraham was asked to sacrifice his only son, whom he loves

  He said, “Take your son, your only son Isaac, whom you love, and go to the land of Moriah, and offer him there as a burnt offering on one of the mountains of which I shall tell you.” (Genesis 22:2).

• Jesus: God the Father sacrifices His only son, whom He loves

  “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life. (John 3:16).

Obedience:

• Isaac: Isaac, we read, carries the wood for his own sacrifice up Mount Moriah with submission to his father’s will

  And Abraham took the wood of the burnt offering and laid it on Isaac his son. And he took in his hand the fire and the knife. So they went both of them together. (Genesis 22:6).

• Jesus: Jesus, we read, carries His own cross with submission to the will of his Father

  and he went out, bearing his own cross, to the place called The Place of a Skull, which in Aramaic is called Golgotha. (John 19:17)

  And going a little farther he fell on his face and prayed, saying, “My Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as you will.” (Matthew 26:39).

Origen, for instance, notes a comparison between Abraham and the God of Jesus Christ. Both are willing to offer their sons in a “magnificent generosity” whereby Abraham offers a mortal son not put to death, and God delivers the immortal son to death. (Walsh, 2012)

The story of Abraham and Isaac is often taken as foreshadowing of the ultimate sacrifice of Jesus.

Isaac, as parabole, is more than a spared son. He now symbolizes the unseen truth of resurrection.¹⁷ The spared son symbolizes that something new is afoot in the divine sphere, which is Christ. Abraham does not merely pass God’s test, and get his son Isaac back; he gets a glimpse of New Testament truth, namely, that someday even the death imperiling his son will have no sting (1 Corinthians 15:55). (Walsh, 2012)

Location:

• Mount Moriah: Traditionally this is believed to be the location of the future Temple Mount in Jerusalem, near where Jesus would be crucified

  Then Solomon began to build the house of the Lord in Jerusalem on Mount Moriah, where the Lord had appeared to David his father, at the place that David had appointed, on the threshing floor of Ornan the Jebusite. (2 Chronicles 3:1).

• Golgotha: The site of Jesus' crucifixion in Jerusalem

  and he went out, bearing his own cross, to the place called The Place of a Skull, which in Aramaic is called Golgotha. (John 19:17).

Most Christian interpreters also presume that Mt. Moriah is in Jerusalem. Caesarius of Arles states outright that the place of Isaac’s sacrifice is where Jesus is later crucified.⁴² Hence, even the story’s very geography is typologically forecasting the future execution of Christ. Luther, however does not think Mount Moriah is in Jerusalem because the entire region around the city is mountainous and it would not, then, have been possible for Abraham to see it from afar (verse 4). (Walsh, 2012)

It was noted above that Christian interpreters view the near sacrifice of Isaac as prefiguring Christ’s crucifixion.⁴⁵ Barnabas is explicit that the sacrifice of Isaac is a foreshadowing of Christ’s passion.⁴⁶ Augustine writes of Isaac,

… the prefiguration was not achieved without bloodshed, in the one case by the slaying of a ram,… In this way the resurrection was symbolized, but the reality of it was reserved for our true Lord. ⁴⁷

Even the poignant detail of verse 6 that “Abraham took the wood of the burnt offering and laid it on Isaac” reminds interpreters like Origen of Christ having carried his own cross on the via dolorosa. (Walsh, 2012)

The third day:

Christian interpreters stress that Abraham arrived on the third day as a typology of the resurrection and even the trinity.⁵³ (Walsh, 2012)

• Abraham: It is mentioned that

  “On the third day Abraham lifted up his eyes and saw the place from afar.” (Genesis 22:4)

• Jesus: Many Christian theologians see this as a foreshadowing of Christ's resurrection, which occurred on the third day after His crucifixion

  that he was buried, that he was raised on the third day in accordance with the Scriptures, (1 Corinthians 15:4).