using System;

public class Program
{
    public class Test
    {
        public DateTime? Date { get; set; }
    }

    public static void Main()
    {
        var test = new Test
        {
            Date = (DateTime.TryParse("string", out var dt) ? dt : null)
        };
    }
}

Date = (DateTime.TryParse("string", out var dt) ? dt : (DateTime?)null)