"做" contains the meaning of "be ", not "become"
"我想做一个警察" means "I want to be a police"
it is "成为" that means "become", not just "成"
(成 is mostly used as a result complement for varieties of verb)
"我想成为一个警察" means "I want to become a police"
how does the word 做 as a singular character have such a broad meaning from ‘doing’ to ‘becoming’ without the addition of another character
As I stated, 做 can mean 'be' but not 'become'
You know when does it mean 'be' or 'do' by looking into the context. When the object after 做 is a task or action, you know 做 means 'do'; When the object after 做 is an identity, you know 做 means 'be'
Example:
做功課，做木工，做好事 = do homework, do woodwork, do good thing (功課，木工，好事 are all nouns for action)
做學生，做木匠，做好人 = be a student, be a carpenter, be a good person (學生，木匠，好人 are all nouns for identity)
Notice: don't confuse 做(do/ be) with 造(make), e.g. 做個包子 (be a bun) is not the same as 造個包子 (make a bun)