When trying to figure out if God exists especially the Christian God you have to understand some of the objectives that He was trying to achieve with creation as this will influence the overall view of things.
God wanted a new type of being, humans, to be in control of their own world with a free will in which to learn about several things including the effects of doing good or bad. Also a place where humans could choose to seek and find God if they wanted to.
To facilitate this a world had to be created in which it would not be observable that the world was manufactured.
The world had to be elaborate, viable and interesting with resources to make things achievable that are advanced.
God had to be hidden so that humans would not feel watched or accountable so that their true nature would be exposed. Also so that humans could feel free to do their own thing and so they could take the initiative and explore. Also so that only people who would want to find God would find him and so that those who would not want to for whatever reason would not be artificially compelled to since they could conceivably conclude that God does not exist and so put themselves at ease.
How do you prove sincerity if you know you are sincere? You can’t really. You can only claim that you are to beings in a free world. Then you wait and see who will trust or believe you. Then work with them and promote them eventually to the highest places. After all if they could trust you in a broken artificial world. They would for sure trust you in the real perfect world when they enter it.