Why did European countries need wealth to start exploring the world?

France, Britain, Spain were the big daddies of Europe, One of their goals was to seek gold silver and other resources out there. The wealthiest of the nations tend to be the most powerful. Another reason was to seek religious freedom. Some also wanted to convert natives to Christianity

Originally it started with people wanting to seek new trade routes for one's nation

Because if they don't have wealth they won't be able to buy their supplies and hire crewmen. They wouldn't be able to get ships and boats.