Can there be true equality when people start from different places in life due to their backgrounds?

Yes. I grew up in a home without heating or air conditioning. We often didn't have running water. Our house was falling apart. So I started in what you could call 'a different place.' But now I am more wealthy than I could have imagined at this point of my life. God has blessed me financially as I've worked hard through multiple jobs. Once I worked 12 hour shifts every day. But through smart choices, taking charge of my education, and working hard, I no longer have to work.
Regardless of race or gender, there is an equality of opportunity in the USA. If you want to make something of yourself, you can.