If the organization is subject to the 85,000 H-1B cap, they can apply for you in April 2014, and if your visa is approved, you can start working on October 1, 2014. However, it is far from clear that this job requires a 4-year degree. See an experienced immigration attorney.
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
Ask them. After all, they offer you a job. They should know.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.