I'm sorry, but I just can't get away from the idea that mankind is God's "experiment". Look at the proof.
There isn't any proof.
There may be incidents/Bible verses that seem to indicate something, but that's not proof.
First, Gods seems to be caught off guard when Adam and Eve sin
Genesis 3:15 - one of Eve's descendants would bruise the serpents head. Both Christians and Jews consider this to be a Messianic prophecy - the difference being that Jews do not believe they speak of Jesus.
1 Peter 1:19 - Jesus is the Lamb slain from the foundation of the world. God provided a Saviour, Jesus, before we ever needed one.
God was not caught "off guard". he knew that Adam would sin, but he already had a plan to save him, and mankind.
Then comes the time of Noah (Genesis 6:6-7) 6 "The Lord regretted that he had made human beings on the earth, and his heart was deeply troubled.
Yes, he was deeply troubled that his creation - those made in his image - had largely chosen to disobey and reject him.
But instead of wiping us out, He continues His "experiment" by allowing Noah and his family to live and replenish the earth.
Well exactly - he didn't wipe mankind out.
Noah, at least, believed in, served and obeyed God. God saved him and his family.
It's interesting that you see this as God choosing to continue with an "experiment"; I see it as God showing mercy to those who loved him.
Noah didn't build the ark overnight - people would have asked him what he was doing and been told that God was going to send a flood to punish them for their sin. They just mocked, and carried on rejecting God.
So, the earth is replenished but most of mankind continues to sin and ignore God.
Many did; not everyone. Even Israel did not ignore God all the time. God sent judges, prophets and kings to lead them - Abraham, Moses, Joshua, Deborah, Gideon, David, Elijah and Elisha, Isaiah, Hosea, Ezekiel etc. etc.
Moving up to the time of Jesus, He makes this statement: John 3:16 - "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life". So, God goes from "I regretted that I have made human beings" to "He so loved the world". That is confusing.
When God led the Hebrew slaves out of Egypt, he led them to Mt Sinai, made a covenant with them and gave them his law. Israel who had been rescued by God, became his people. Throughout the OT however, Israel broke their covenant with God - not just once but again and again. Each time God punished, or corrected, them, they repented, he forgave them and restored them. Read Hosea 11 for an example of God's love for his people.
Finally, God said that he was going to make a new covenant with his people, Jeremiah 31:31-34. They were incapable of keeping the old one and many thousands of animals were being sacrificed in an attempt to atone for their many sins. The sacrifice for sin, or guilt, was a perfect lamb (in some cases, goat). When Jesus came he lived a perfect life. He was the Lamb of God who gave his perfect life for the sins of the world, John 1:29. Before he died he told his disciples that his blood was the blood of the New Covenant poured out for the forgiveness of sins. Hebrews 10:1-18 explains how Jesus' sacrifice was made once, for all.
I believe in God and the Trinity, but I just don't get His plan for mankind.
He wants people to know and believe in his Son.
Today there are billions of people who are lost, and I just don't understand why He continued His experiment, only to send billions to annihilation.
What makes you think that our creation was "an experiment" in the first place?
"Experiment" suggests that someone doesn't know what will happen and they want to find out. God knows everything.
I don't believe God annihilates anyone.
I try to visualize the day of judgement with billions standing before Jesus and that one person in the midst of those billions who will be judged.
Who are the "billions" who will stand before Jesus - Christians, or unbelievers?
Who is the one person in those billions who will be judged?
How can that one person be judged in the midst of billions?
I don't get what you're asking.
If you're saying that the "billions" are unbelievers and only one in so many billion will be a Christian, what evidence do you have that that will be the case?
If you are saying that the billions are all the people who have ever lived and the one person being judged will be Jesus, that is completely wrong and I think you need to go back and read the NT.
Jesus won't be judged; he never did anything wrong. People who do not know Jesus as their Saviour will be judged. People who once knew Jesus but rejected him, or were given an opportunity to meet Jesus but did not take it, will be judged, maybe more severely. Christians who believe in Jesus and have eternal life, will be asked to give an account of their lives, but will not be judged for their sin - Jesus has taken that and they have received his forgiveness.
Who exactly will be judged - eg babies and people who never heard the Gospel - and what criteria will be used, is unknown and best left to God.