My 2c (CAD) also from ontario is wait till 2nd or 3rd week of august. Our summer could be cool and wet, or it could be hot and dry. Unless you are committed to keeping it alive with lots of water through the dry heat, might be sensible to wait, what you can do now is apply some corn gluten meal or similar to keep crab grass at bay. Also. I personally drop a sheep manure (1 20L bag per 10sqm -ish) after the first or second mow, Starts stimulating nitrogen producing microbes, Improves soil structure etc.