The book of Hebrews depicts the risen Christ in the three-fold function of Prophet, Priest, and King (Heb. 1:2-3 & 7:3). He is the only Mediator between God and men (8:6). He intercedes for and saves all who come to God through him (7:24-28). As for Christ being Apostle alongside being Priest, that is also true - Heb. 3:1.
But he is not just one amongst a number of prophets, priests, kings, mediators and apostles. He is our great High Priest. He is King of Kings. He is the only Mediator who enables us to approach God. He chose the apostles who accompanied him during his earthly ministry. The twelve whom Jesus chose were his apostles (Luke 6:13). The relationship is of Christ being The Apostle who chooses men who will be apostles in his Church (Ephesians 4:11). But it's not as if God requires his Son to be his apostle, as the question seems to put it (unless I've misunderstood.)
The men who were apostles on earth bore witness to Jesus Christ, crucified, resurrected, and coming again from heaven. "You will be MY witnesses..." Jesus commanded them (Acts 1:8). Jesus, on earth, showed them the Father by doing the Father's will, and sharing with the disciples all the words the Father had given him (John 15:15-16). "He that hath seen me hath seen the Father" he explained - not literally of course - see John 14:6-11.
So, Christ is The Apostle, just as he is The great High Priest, and that for our benefit, not God's. Christ is not Apostle to God, but to those who belong to Christ by faith: "Jesus, the apostle and high priest of our confession" Heb. 3:1.
You ask, "Did God sen[d] his son as an apostle to bear witness of the father?" God sent his Son to bear witness of the Father, and all who believed the Son's witness discovered Jesus to be their Apostle, just as he became their King, their Redeemer, their Saviour, their great High Priest and their Mediator. All the benefits are towards those who make the good confession of faith in Christ. Those thus benefited then become witnesses of Jesus Christ.