The short answer to this question is "yes".
God did send his son to die– Galatians 4: 4-5, “But when the fullness of the time came, God sent forth His Son, born of a woman, born under the Law, so that He might redeem those who were under the Law, that we might receive the adoption as sons.” 1 John 4: 9-10, “By this the love of God was manifested in us, that God has sent His only begotten Son into the world so that we might live through Him. In this is love, not that we loved God, but that He loved us and sent His Son to be the propitiation for our sins.”
Jesus also volunteered to be the one to die. John 10:11-18, “I am the good shepherd; the good shepherd lays down His life for the sheep. He who is a hired hand, and not a shepherd, who is not the owner of the sheep, sees the wolf coming, and leaves the sheep and flees, and the wolf snatches them and scatters them. He flees because he is a hired hand and is not concerned about the sheep. I am the good shepherd, and I know My own and My own know Me, even as the Father knows Me and I know the Father; and I lay down My life for the sheep. I have other sheep, which are not of this fold; I must bring them also, and they will hear My voice; and they will become one flock with one shepherd. For this reason the Father loves Me, because I lay down My life so that I may take it again. No one has taken it away from Me, but I lay it down on My own initiative. I have authority to lay it down, and I have authority to take it up again.”
Also, in Hebrews 7:26-28, “For it was fitting for us to have such a high priest, holy, innocent, undefiled, separated from sinners and exalted above the heavens; who does not need daily, like those high priests, to offer up sacrifices, first for His own sins and then for the sins of the people, because this He did once for all when He offered up Himself. For the Law appoints men as high priests who are weak, but the word of the oath, which came after the Law, appoints a Son, made perfect forever.”