The correct answers are We don't have much time before the guests arrive! and We don't have a lot of time before the guests arrive!

In this context, "time" is an uncountable noun. We use "much" or "a lot of" with uncountable nouns, especially in negative sentences. "Many" is only used for countable nouns, and we do not add an "s" to uncountable nouns like "time" (unless we are talking about the number of occasions, e.g., "I told you three times").