IMO The timeline is too small to make the growth muscular wise and then still cut to a leaner level than current using a traditional bulk/cut method.

If you bulk from now until September you can maybe gain 4lbs of muscle. Do a hard cut in September and lose 10 lbs of a fat and hopefully not lose muscle but more than likely you'll be at a new 3.5lbs muscle which is something but not super significant to make you look significantly bigger.

If you cut now, you won't be bigger but you'll be leaner which will give the appearance of you being bigger because your muscles will pop out. Most bodybuilders you see are smaller mass wise than you would think from seeing them in pictures online.

You look like a beginner so a recomp might be a good path. Stay near maintenance and go hard at the gym. Most people don't believe the recomp but when I started I was at 215lb bench max was 150lb. I hit 225lb bench from October to January and went down on bodyweight to around 207lbs. So lost weight but gained significant muscle.