Mathematically, a first-past-the-post system will inevitably result in a two-party system (perhaps with the occasional success of a regional party).

There is nothing you can do within the system to change that - you can only vote for the party that better reflects your views (and pressure them to continue to do that).

The thing you do to dismantle two-party politics is advocating for other electoral models: proportional representation; single-transferrable vote or approval voting; etc.