Grass seed germination time varies depending on a bunch of factors, like what variety(s?), temperature etc. I had to look it up, because even though I have a degree in botany and even had a whole class devoted to turf, it was my least favorite class, so I didn't retain much of anything. (Despite that time in my life being some 25-30 years ago, I actually and shockingly retained quite a bit, especially Latin names, oddly enough(!) Yet I usually don't really know what month it is, or what or if I ate(!) Lol, I suppose given the choice, I'd rather remember the Latin names anyway... Lunch is fleeting. )

I also had to look up because you are in a different type of climate with different types of grasses than are familiar to me. Do you know what type of grass it is? Of southern types, one site I looked up said: Bermudagrass 5-12, Centipede grass 10-28, Bahiagrass 14-28, Zoysiagrass 10-21. These are general guidelines of course, but at least they should give you some idea. Remember that not all seeds will germinate simultaneously, so be sure to continue the watering even after the sprouting gets going to get your best results.