Store timestamp with time 00:00:00

For safety just let Carbon decide the end or the start of the day using ->endOfDay() or ->startOfDay(). Choose what suits you more.

Carbon::createFromFormat('d-m-Y', $date_interval["start_date"])->endOfDay();
Carbon::createFromFormat('d-m-Y', $date_interval["start_date"])->startOfDay();

I've usually set the date with the call, and then reset the time to 00:00 with

Carbon::setTime(0, 0, 0);  // from the parent, DateTime class

In the class, there is also a Carbon::startOfDay() method that will set the appropriate values.

public function startOfDay()
{
    return $this->hour(0)->minute(0)->second(0);
}