"When will you start thinking?"
Translation:Πότε θα ξεκινήσεις να σκέφτεσαι;
Maybe θ' αρχίσεις should be accepted too. This is, in any case, the more common way of writing Greek.
This action is not a one time action. In English, we need a gerund. In Greek, we need Present Subjunctive. This post here https://www.duolingo.com/comment/24471413 will help you understand the Subjunctive concept a little bit better. If you have any further questions/concerns, feel free to ask. ^.^
Usually, αρχίζω να doesn't quite mark a one time action. Mostly because when someone says that they'll start doing something, they imply that they'll also keep on doing it Ι'll start eating healthy, I'll start going to the gym etc)