Trust, faith and belief are synonyms. Trust is a powerful thing. When we say we trust someone or something, it affords it the character of being trustworthy. This is true of living beings as well as inanimate objects. If I trust a bridge, I am putting my faith in a structure to hold the weight of whatever I put upon it. I trust it enough to walk over, to drive a vehicle on top of it, or to be undaunted that traffic transverses it daily. I have faith in that bridge.
When we say we have faith in God, or we believe in Jesus, what we are saying is that we are confident he is fully capable to do what we trust him for, namely to save us. Like a bridge, faith in Jesus is to trust he will support us to cross over to the other side.
Trust is usually not given, but earned. We don't altogether trust strangers (for good reason) and we certainly don't trust those who have demonstrated themselves to be untrustworthy (for even better reason). I would not hand a newborn baby to a complete stranger nor would you entrust your kids to a lady with a pattern of abuse of children. You wouldn't pass your house keys to a man you just met, nor would I to a convicted house burglar. Their trust has not been earned.
With God, we have one who has shown himself to be trustworthy not just to us, but to all his people throughout history. That is one reason, among many, we still look to the Hebrew Scriptures and God's covenant faithfulness to ancient Israel. It demonstrates to us the character of the God we trust with our lives. Two millennia of church history are replete with evidences of the trustworthiness of God. Christians throughout Christendom have trusted him with their lives, even unto death, and have found satisfiction in that faith. God's faithfulness, like a story's throughline, can be seen in history's pages, chapter after chapter.
When we say we believe in God, that is not a statement of mere philosophical conjecture. It is not the simple antonym of atheism. It is a dynamic statement of trust. We have faith in Jesus as Redeemer, we trust his sacrifice on the cross and power in the resurrection will be sufficient to save us from judgment. We trust him as King, he reigns over our future as well as our past. We trust him as the bridge we know will uphold us towards life.