Is there a limit on how early you can apply for COE (student ) ?

I was accepted into university in Japan and was suppose to revived my COE and fly off to intensive Japanese class offer by university in October . But the immigration just notify my university early that they “not permitted” my COE for language class because I already max out my two year of language study .
My university reassure me that this won’t impact my place in the degree program and say immigration will still give me visa for the degree study that start in April next year.
Here what concern me
My university say they will summit my COE application for the degree study in December but from my past experience and research show that Jan-March is busiest time of year for immigration so I fear that my COE will get delay if my university will submit my application in December .