Question regarding very limited use of marijuana

I applied for a job where it is necessary to have a security clearance, the interview went extremely well and I was honest about previous drug use (marijuana less than 5 times, during graduate school, last time being March of 2014) and the employer said he would be willing to sponsor me when I had enough time to start the security clearance process.
I have a very clean record, was never caught nor would I have had this in my system if had to take a test but was forthright about it and honest. It was a stupid decision that I made in graduate school, and I certainly do not plan on doing it again in the future. What is the earliest date that paperwork could be started for a security clearance?

Thank you in advance

There is no set amount of time for abstinence, but rather the extent of use, type of drugs, circumstances, etc… The position and agency may determine whether the length of time since last use is sufficient.