The visibleStart() method returns the start of the first visible day.
DayPilot.Date object
var dp = new DayPilot.Calendar("dp");
// ...
dp.startDate = "2019-01-03"; // Thursday
dp.viewType = "Week";
dp.weekStart = 0; // Sunday
dp.init();
var start = dp.visibleStart(); // Sunday, 2018-12-30T00:00:00