Rick is correct. It is extremly unprofessional for a company to expect you to quit an employer without any notice.
Another thing, if a company extends your start date, start looking for a new job (but don’t quit). When I graduated B-school, the company I was going to start with pushed my date back 4 months. I still ended up working there for about 18 months, but I asked for them to give me my signing bonus immediately, under the petense that I already quit my job and was not prepared to be out of work that long. That way, if the offer evaporated (which happened with some similar companies) I still had money in my pocket for doing nothing.