The Sim chase starts on a set date, the current one started on the 10th of August the previous on the 21st of July, always at 7AM UTC (unless it starts directly after a new DLC update, those updates hits stores at 22.30/10.30PM UTC on given dates)
First time you open the game after 7AM UTC (or a DLC update) on the stated date, the chase will start
The official blog will have the dates when they will start https://www.ea.com/games/the-sims/the-sims-freeplay
If you know that a Sim chase will start, you can wait to open your game until a time when it will suit you to reset the chase days. This also goes for Craft Challenges and Influence Island
For me, 7AM UTC is currently 9AM CEST so that is a good time for me (better when the daylight savings end and 7AM UTC becomes 8AM CET). For a friend on the east coast of the US 7AM UTC is currently 3AM EDT and they prefer to wait to open their game until 7AM on those days, instead of opening it right after waking up around 5.30AM - 7AM is a bit early for me but each to their own - POINT IS, YOU CAN CONTROL WHEN THE RESET TIME IS FOR YOU IF YOU PLAN AHEAD