If you're adopting a relatively formal written style, especially an academic style, it makes sense to choose to include that. But it is not required by the rules of grammar.
In examples like yours, that is a subordinator marking a content clause. It lets the reader know that the clause they're reading is subordinate and not a main clause.
Most of the time, that can be omitted from content clauses. That's because the reader can figure out from the structure of the sentence whether it's a subordinate clause or not.
In your example it's fine either way:
1a. Assume [ that you are given a ball ].
1b. Assume [ that you are given a ball ].
The reader knows assume must be the main clause verb, so you are given a ball must be a subordinate clause. There's no other possibility, so that is an unnecessary signal.
However, if the subordinator that comes before the main clause verb, it cannot be omitted:
2a. [ That you are given a ball ] can be safely assumed.
2b. *[ That you are given a ball ] can be safely assumed.
At the beginning of a sentence, you need that to let the reader know they're reading a subordinate clause and not a main clause. As a result, sentence 2b is ungrammatical.
There are two types of relative clauses in English, which I shall call 'defining clauses' and 'commenting clauses'. They are best described with an example:
Pilots who have dull minds seldom live long
Pilots, who have dull minds, seldom live long.
The first sentence is a warning about the dangers of having a dull mind if you want to be a pilot. The second is insulting to all pilots.
Defining clauses are never separated from the main sentence by a comma: commenting clauses always are.
There's an old fashioned rule that you should always use 'that' rather than 'which' when you are writing a defining clause. Thus
Animals that lay eggs are called birds.
is grammatical, while
Animals which lay eggs are called birds.
is ungrammatical. These days, however, prescriptivism (language rules) is unfashionable and people are far more likely to consider both sentences to be grammatical, and to mean the same thing. Moreover, in colloquial speech, and even in writing, the rule has never been universally followed.
Of course, neither sentence is factually correct: a snake lays eggs, but is not called a bird!
Best Answer
The best choice would be: