Do I need to apply with the government to receive a General License?

No, you do not. Current regulations state very clearly that a person travelling to Cuba on a General License may do so without needing to write in to OFAC for a letter of specific authorization as quoted from OFAC regulations below:

No. No further permission from OFAC is required to engage in transactions by a person who meets all criteria in a general license. Individuals wishing to engage in activities that may fall within the scope of a general license should review the relevant general licenses contained in the CACR to determine whether their travel-related transactions are covered by such general licenses. Persons subject to U.S. jurisdiction who wish to engage in any travel within the 12 categories of activities specified in the CACR that does not meet the requirements of a general license will need to apply for a specific license from OFAC.