I'm currently doing some experimenting in my 3 car oversized garage (6 inch insulated walls) which tends to get hot during the day and stay hot all the time because of the 90+ heat we've been having every day here in Indiana.
I put a in-window fan in each of 2 windows on opposite corners of the garage with one pulling air in and one taking air out.
The goal is to run the fans at night so the garage gets cooled down sufficiently, then shut them off in the morning and rely on the insulation to keep it livable during the day.
I'm only about a week into my tests, and the heat last week was as bad as we've had in a while, with night time temperatures only reaching the low 70's.
To this point, I couldn't recommend this approach. I'm turning the fans on about 11:00 PM with the garage 90-degrees and it's still 80 outside. Getting up in the morning with the garage 80 degrees and it's 74 outside. By 4 PM the garage is 90 again.
I'm going to continue to experiment with this. This week the highs are supposed to be more mid-80's and the lows into the 60's. For my plan to work, I really need it to get cool enough outside to get enough cool air blown through the garage to cool off not only the air inside but the walls and floor too.
To the OP....if your mini split had enough cooling capacity, it would keep up. But, the energy cost to do that might be prohibitive. I'm considering going to a mini-split in my garage as well, but I just got a $450 electric bill for the attached house and the bonus room above the garage which has it's own 3 ton AC. So adding an additional "meter spinner" is not something I'm wanting to do.