As proof that Jesus is the Messiah, he was resurrected in 3 days and 3 nights (Matt. 12:40 ). Similarly in John 2:18-21 “Then answered the Jews and said unto him, What sign shewest thou unto us, seeing that thou doest these things? Jesus answered and said unto them, Destroy this temple, and in three days I will raise it up. Then said the Jews, Forty and six years was this temple in building, and wilt thou rear it up in three days? But he spake of the temple of his body. When therefore he was risen from the dead, his disciples remembered that he had said this unto them; and they believed the scripture, and the word which Jesus had said.” Read also Matt 16:21; Matthew 26:61; 27:40;Mark 14:58; Mark 15:29; Acts 6:14

Also, while it is true that his resurrection gives the “adulterous generation”(Matt. 12:39; 16:4) proof that Jesus is the Messiah, the reasons for his resurrection may even be more far-reaching. Aside from being a proof, the following verses give us an inclination as to why:

Rom. 5:6-10″For when we were yet without strength, in due time Christ died for the ungodly. For scarcely for a righteous man will one die: yet peradventure for a good man some would even dare to die. But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us. Much more then, being now justified by his blood, we shall be saved from wrath through him. For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.”
The preceding verses show that the purpose of his death is to reconcile us to the Father since “all sinned“, as in:

Rom. 3:23-26“For all have sinned, and come short of the glory of God; Being justified freely by his grace through the redemption that is in Christ Jesus: Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.”

Jesus, being dead means exactly that… dead completely, not alive. And, without him being resurrected or be alive he would still be dead and would not have received the promise by the Father of the Holy Spirit to in-dwell in us, meaning “saved by his life” (Rom.5:10).

And, John 16:7 is clear that Jesus has to be resurrected, be alive, to go to the Father to get this promise of the Holy Spirit and subsequently to dwell in us. Notice, “Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.”
As to the question who is that God who resurrected Jesus? Was he the Father or the Son or the Holy Spirit? In New Testament times, when the word “God” is mentioned, it refers to the Father to differentiate it from Jesus, the Son of God (the Father). Consider then the following:
Galatians 1:1 “Paul, an apostle—sent not from men nor by a man, but by Jesus Christ and God the Father, who raised him from the dead.”
The apostle Peter stated in his first sermon on the Day of Pentecost: “This Jesus, God has raised up, of which we are all witnesses” (Acts 2:32). Subsequently, in Acts 3:15, he told his audience that they had “killed the Prince of life, whom God raised from the dead, of which we are witnesses”.

The apostle Paul also testified in Acts 13:33; compare verse 37: “God has fulfilled this for us their children, in that He has raised up Jesus”. Continuing now in Acts 17:31“Because He [God] has appointed a day on which He will judge the world in righteousness by the Man [Jesus] whom He has ordained. He has given assurance of this to all by raising Him from the dead”.

Ephesians 1:20 ” …he raised Christ from the dead and seated him at his right hand in the heavenly realms,”

But what about John 2:19; see verse 21 also when Jesus said, “Destroy this temple [referring to His body being slain], and in three days I will raise it up [implying His resurrection]”. If Jesus meant by this that He would come back to life on His own, he contradicted other testimonies. Rather, after God the Father brought life back to him while in the tomb, He would stand up and “raise it up” himself from his lying down to then get out from the grave.

Similarly, the same mechanism will apply to us. The Spirit of God gives power. The Father gives the Holy Spirit that brings about life. And by so giving that spirit of life, this is the power we will then be resurrected with. As Paul tells us, “If the Spirit of him who raised Jesus from the dead dwells in you, he (the Father) who raised Christ from the dead will give life to your mortal bodies also through his Spirit that dwells in you” (Romans 8:11, NRSV).

Clearly, it was God the Father who did it as promised by him to YHVH/Creator before the foundation of the world and before the latter incarnated into man-Jesus. The “faith of Jesus“, as referred to in Rom. 3:22, Gal.2:16, 3:22, and Phil. 3:9, is faith “in” someone. There is nobody else to whom the Son can defer to (I Cor. 15:24-28) but to his Father who knows everything(Mk. 13:32). This faith “of” Jesus is faith “in” his Father who he knows will deliver everything he promised. Everything was planned by the Father and was/will be executed by his Son(I Cor. 8:6). They are “one” as they are together in everything, as we will be “one” with them(Eph. 4:6).