Which country are you from? I would suggest that, if you are from a country on the list below, that you simply arrive on a visa-exempt entry stamp for 90 days. If there is no chance that you are going to be converting into an ARC, and you don’t absolutely need the student visa for anything, then there’s no point in laying out the cash & making a trip to the consulate for the visa. In this case, if you entered on June 15th, 90 days would mean you need to leave on or before September 13th.
However, if you do want to go ahead and get the visa, or are not from one of the countries below, apply within 3 months (90 days) of your documented start date. That would mean sometime between April-June. The student visa will allow entry within 90 days from the date of issue, and as long as your program is less than 90 days away from starting, there won’t be any problems issuing the visa. The student visa generally speaking will be 60 days, extendable to 180 days in 60-day increments. So, you could enter June 15th, extend your visa 60 days in early August, and stay until September 15th - no problem. To extend the visa, you’ll need to bring a copy of your enrollment documents and passport to the local National Immigration Agency branch.
90-day visa-exempt countries list:
“The nationals of the following countries are eligible for the visa exemption program, which permits a duration of stay up to 90 days：Austria, Belgium, Bulgaria, Canada, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israeli, Italy, Japan, Republic of Korea, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Monaco, the Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, U.K., U.S.A., and Vatican City State.”