In this sentence, you could say that "since the beginning of time" is cliched. It is certainly an exagerration. Perhaps you could instead say something like "For centuries..."
Today, the word "Negros" would be seen as a biased word, or at least one that is not very respectful or polite. Therefore, you should probably replace it with "African Americans."
The word "strived" might be seen as a biased word since it seems to imply approval of what the "Negros" have done. However, it would be hard to find a word that can't be seen that way. "Worked hard" has good connotations. So have "struggled" or "fought."
So, I would write this as something like "For centuries, African Americans have struggled for equality with whites."