I think grammatically in English that would be incorrect. Because time always 'exists', you/a person may not have time to do an activity but it exists none the less.
So a more appropriate translation could be: I do not have time.
Meaning if someone asked can you buy me bread on your way home? The response could be: I don't have time I won't be able to buy it.
If an English speaker says "I don't have the time," it can mean either "I am too busy," or "I do not know what time it is." If you eliminate the article "the" and just say "I don't have time," it always means too busy.
This is a really good question, English articles are tricky.