Is there such a thing as a safe time, that one will not get impregnated?

Yes. You need to have regular, predictable, consistent cycles. If you do, you can calculate when you ovulate and avoid intercourse starting a few days before ovulation to a few days after.
No. If when you say safe you mean 99-100%: in theory 'yes, ' in practice a big 'no.' this is called the 'rhythm method' and has a failure rate of around 30% at best, often much worse.