Can you explain what you mean by “shows up?” My Tasks can be set up in many different ways, so it’s not clear how it is set up in this case and falling short.
You can have a My Tasks tab sorted by Start date that certainly will address this.
Some other related info, and places where you can vote for added functionality:
A link to my article on My Tasks set up which provides rules for getting notified early about upcoming Start and Due dates:
Please consider voting for this:
More info, particularly toward the end of the thread: