Having to push back arrival date - did I miss my window?

I've been wanting to visit Sardinia for a couple weeks for a few years now. I had plans to arrive on the 4th and stay until the end of the month, but due to unforeseen circumstances I probably won't arrive until the 15th or later.

I have no qualms about rescheduling he trip to next year if needed - I have a flexible budget and time so that's not the issue. My goal is just to visit the island at the absolute primetime, and I had been told that that was early September. Did I miss my window? Will arriving the last weeks of September mean Sardinia won't be "at it's best"?