How do Trinitarian Christians explain this to people who neither understand nor believe the Trinity?
As an orthodoxly trinitarian Christian, I can only answer by saying how I would answer a non-trinitarian-believing person who asked the question, ‘Who resurrected Jesus – the Father, the Son or the Holy Spirit?’. This would not be with a view to getting them to believe this doctrine, but purely to arouse a sense of wonder at the awesomeness of God. I hope other trinitarian Christians add further insights into how such a question could be answered, for my answer is by no means complete.
The simple answer is that all three resurrected Jesus. It did not have to be one of the ‘persons’ in the Godhead, or two of the others. The entire Godhead was equally involved in this unique resurrection, the likes of which had never happened in all creation, up till that time when the crucified Christ was raised in triumph from the grave. That is why Christ is called “the firstborn from the dead” (Colossians 1:18). Others had been resurrected in Old Testament times, and Jesus had also resurrected a few individuals before he died himself. But all of those ones were raised as human sinners who would have to die again, as mortals. Not so with the crucified Christ, who died sinless. Death could not hold him, for death can only claim sinners. As the Son of God, he gave himself over to death as a sacrifice to God, trusting in the promises of the Father for his resurrection (as in Psalm 16:10), with a living faith.
Hence the resurrection of the Lord Jesus is based on His Life. Due to
a deathless life in Him, He cannot be held by death... Only what is of
God can be resurrected... Whatever is of Adam cannot live upon its
going into death. But the life of the Lord is quite able to pass
through death and come out again. This is resurrection. - Christ the Sum of all Spiritual Things ch. 2, Christ is the Resurrection and the Life, Watchman Nee (CFP Pub. Inc, NY, 1973)
Consider what Jesus said to Martha: “I am the resurrection and the life” (John 11:25). Notice what he did not say about her brother’s death and resurrection. Jesus did not say “I will resurrect and give life…” (for he intended to resurrect Lazarus). No, he claimed to BE – in his own person – The Resurrection and The Life. Christ already had resurrection power in him, before he submitted to death. That is why he could say what you cited (John 2:19-22 and 10:18). He had authority to both lay down his life and to take it – his life – up again. He would raise the temple of his body in three days. He would do it because he had the authority as being The Resurrection and the Life.
This authority came from the Father, as Jesus explained: “…the world must learn that I love the Father and that I do exactly what my Father has commanded me” (John 14:31). So, when Jesus raised himself from the dead, he was ‘only’ doing what his Father had commanded him to do! And that was done in the power of the Holy Spirit. This inter-relatedness and co-operation of the three ‘persons’ of the Godhead is again shown here, when Jesus said “All that belongs to the Father is mine. That is why I said the Spirit will take from what is mine and make it known to you.” (John 16:15)
The resurrection of Christ was not an independent act of the Father. It was not an independent act of the Holy Spirit. It was not an independent act of Christ. All three were equally involved with the unique miracle of the crucified Christ being resurrected.
That is why, as your comments detail, Acts 2:24 says that God raised Jesus from the dead, confirmed in Romans 6:4 which says Christ “was raised up from the dead by the glory of the Father”. That is why Romans 1:4 says that Jesus was, through the Spirit of holiness, declared with power to be the Son of God by his resurrection from the dead, and 1 Peter 3:18 says Jesus was put to death in the body but made alive by the Spirit.
There is no contradiction. All three ‘persons’ of the Godhead combined in perfect oneness of purpose to fulfill the prophecy in Psalm 16:10, that God would not let his Holy One be abandoned to the grave or see decay there, quoted by the apostle Peter in Acts 2:24-31:
“But God raised him from the dead, freeing him from the agony of
death, because it was impossible for death to keep its hold on him.
David said about him, ‘…you will not abandon me to the grave nor will
you let your Holy One see decay…’ Seeing what was ahead he [David]
spoke of the resurrection of the Christ, that he was not abandoned to
the grave nor did his body see decay. God has raised this Jesus to
life, and we are all witnesses of the fact.”
The resurrection of Christ provides an insight into the awesome harmony and equal power of the three ‘persons’ in the Godhead. Every time God is credited with resurrecting Christ, the whole Godhead is incorporated into that praise.
That is how I would explain the matter to a non-trinitarian-believing person asking about who raised Jesus.