Let's analyze this not-a-sentence:
Polizeigewalt hat gegen Schwarze schon immer gegeben.
- Polizeigewalt (police violence)
an accusative object (Wen hat es gegeben?)
This is NOT the subject! A subject always has to stand in nominative case (details below)
- hat ... gegeben (did exist)
the predicate (What is the action? What is going on in this sentence?)
- gegen Schwarze (against black people)
a prepositional object (Wogegen hat es Gewalt gegeben?)
- schon immer (for ever)
a predicative supplement
So we have a predicate plus supplement, and two objects. But there is no subject! Polizeigewalt is not the subject. By accident the nominative case and accusative case look equal at this word (which is true for most German words), but if you replace it with a masculine word, and add an article, it becomes obvious:
wrong: Der Kampf hat gegen Schwarze schon immer gegeben.
correct: Den Kampf hat es gegen Schwarze schon immer gegeben.
The word es is just a grammatical placeholder for the subject. It is called "expletive subject" (if you talk about the grammatical function) or dummy pronoun (if you talk about the word class), and you have it in english too:
What is this "it" that rains? It's nothing. It's just a grammatical placeholder for the subject, and the es in many German sentences has exactly the same function
What also might disturb you, is the fact, that German doesn't have an SVO word order like English (SVO = Subject, Verb, Object in this sequence). German has a V2 word order (V2 = Verb at position 2), while all other parts of speech can almost freely float through the sentence.
The most common place for the subject is position 1, which results in an SVO order like english, but also other parts of speech may occupy position 1, like the accusative object Polizeigewalt did in your sentence.
You can move the subject to position 1, which might give you a more comfort feeling:
Es hat schon immer Polizeigewalt gegen Schwarze gegeben.
There always was police violence against black people.
If you convert this sentence into Präsens (and delete schon immer, because "for ever" doesn't make much sense in present tense) you get:
Es gibt Polizeigewalt gegen Schwarze.
There is police violence against black people.
And the word "there" in the english sentence also is an expletive subject. It's the same as in german. The word "there" doesn't refer to any place. I t is just a grammatical placeholder.