The Gospels anticipated an Inter-advent period

I believe Jesus' priority at his first coming was to Israel.  

Ideally, if Israel would have responded positively to Christ at his first coming, they could have gone to proclaim him to the Gentiles.  

Of course, Christ's rejection by Israel--as foretold in the Scripture: the "stone the builders rejected"-- is figured into as to how both Jew and Gentile would be saved: by his death on the cross.  

He had to come and present himself so that Israel could either accept or reject him:  the extent of the rejection (being the greater number of Jews and Jewish leaders) would figure into God's purpose for the inter-advent period (as indicated in the parables of the "mystery of the kingdom").  

What Jesus said to the Canaanite woman expressed his priority to Israel, and his *dog reference, I believe was just an analogy that one's children are fed before one's dog, but the woman acknowledged that and responded she'll accept whatever he has left over (just like even the dogs eat what falls from the master's table).  

The Gospels anticipated an inter-advent period, though it could have been fulfilled by the remnant of believing Jews, God chose to create a new people for that period of Jew and Gentile (the "church")--which wouldn't be fully grasped (understood) right away.  

Israel as a nation would be judged and not be restored as a nation until after the Second advent.  

Things in the Gospels that involve the inter-advent period apply to the gentile-Jew assembly (Great Commission, baptism, Lord's Supper, parables of the mysteries of the kingdom), since national, geographical Israel is not the people for God's purpose at this present time.   

*²¹ Then Jesus went out from there and departed to the region of Tyre and Sidon. ²² And behold, a woman of Canaan came from that region and cried out to Him, saying, "Have mercy on me, O Lord, Son of David! My daughter is severely demon-possessed."

²³ But He answered her not a word.

And His disciples came and urged Him, saying, "Send her away, for she cries out after us."
²⁴ But He answered and said, "I was not sent except to the lost sheep of the house of Israel."
²⁵ Then she came and worshiped Him, saying, "Lord, help me!"
²⁶ But He answered and said, "It is not good to take the children's bread and throw it to the little dogs."
²⁷ And she said, "Yes, Lord, yet even the little dogs eat the crumbs which fall from their masters' table."
²⁸ Then Jesus answered and said to her, "O woman, great is your faith! Let it be to you as you desire." And her daughter was healed from that very hour. Matthew 15:21-28