On normal mode, as mentioned by others, it is possible to grind levels, you just need to be aware of a few things when hammering out those levels.
You are correct that there is a limited number of days before the "so-called War Phase", you have about 12 months depending on your choices in game, but each day off (once a week) you get to choose if you want to battle or do other things, you almost always have the choice so there is no certain days you have to grind.
Of course there are more optimal days to grind, such as days with Rare battles, but you'll see those well in advance when you start each new month and can plan how you will play the month out.
When selecting to do Battle on your day off, you are given a set amount of Battle Points, dependent on your Professor Level.
You will be presented with a large map and on the right is a list of all available battles for that day.
On normal mode only, there is one selection that will not use up any Battle Points, this option is the only one to not have a big red sword icon on it.
This battle is repeatable, seemingly as many times as you want, I myself tested it just 3 times.
The other options are not "grindable" as they will consume a Battle Point each when selected.
Once you run out of Battle Points, your day off ends, and you will continue advancing through the calendar.
This will allow you to grind for level if that is what you need, however to advance to better classes and gain more stats you will need your students to complete exams, which they can only do on the "Day Off Menu", at the start of each of your days off.