Do some people have a spiritual head start from birth?
Yes, people are gifted differently, spiritually as well as physically. But God asks each person only to make full use of what they have been given, and He judges by that measure. So no one is treated unfairly.
The answer becomes clear when we look at the body. Not everyone has the same build, the same strength or the same beauty. People are born with very different gifts. It would be strange if the spiritual side were any different. There too people begin at different points, just as the hadith above speaks of gold and silver.
But God does not measure who ends up standing highest. He looks at what a person has made of what they were given. True excellence in God's eyes means using one's own abilities to their very limit. What matters is the ratio between what one has received and what one does with it.
A person with great abilities who makes little of them falls short of their potential. A person with smaller abilities who gives everything they have is counted as excellent by God. That is why the first verse above says that no one is burdened beyond their capacity. Each person is measured by what they are able to bear.
So no one has reason to complain. The differences between people are, as the second verse above says, a test. Whoever has received much carries more responsibility. Whoever has received less is not at a disadvantage. A head start at birth does not decide a person's worth before God.