There is a way. Add these classes: 
DefaultDateTimeValueAttribute.cs
using System;
using System.ComponentModel;
using System.ComponentModel.DataAnnotations;
using System.Linq;
using System.Reflection;
using System.Runtime.CompilerServices;
using Custom.Extensions;
namespace Custom.DefaultValueAttributes
{
    /// <summary>
    /// This class's DefaultValue attribute allows the programmer to use DateTime.Now as a default value for a property.
    /// Inspired from https://code.msdn.microsoft.com/A-flexible-Default-Value-11c2db19. 
    /// </summary>
    [AttributeUsage(AttributeTargets.Property)]
    public sealed class DefaultDateTimeValueAttribute : DefaultValueAttribute
    {
        public string DefaultValue { get; set; }
        private object _value;
        public override object Value
        {
            get
            {
                if (_value == null)
                    return _value = GetDefaultValue();
                return _value;
            }
        }
        /// <summary>
        /// Initialized a new instance of this class using the desired DateTime value. A string is expected, because the value must be generated at runtime.
        /// Example of value to pass: Now. This will return the current date and time as a default value. 
        /// Programmer tip: Even if the parameter is passed to the base class, it is not used at all. The property Value is overridden.
        /// </summary>
        /// <param name="defaultValue">Default value to render from an instance of <see cref="DateTime"/></param>
        public DefaultDateTimeValueAttribute(string defaultValue) : base(defaultValue)
        {
            DefaultValue = defaultValue;
        }
        public static DateTime GetDefaultValue(Type objectType, string propertyName)
        {
            var property = objectType.GetProperty(propertyName);
            var attribute = property.GetCustomAttributes(typeof(DefaultDateTimeValueAttribute), false)
                ?.Cast<DefaultDateTimeValueAttribute>()
                ?.FirstOrDefault();
            return attribute.GetDefaultValue();
        }
        private DateTime GetDefaultValue()
        {
            // Resolve a named property of DateTime, like "Now"
            if (this.IsProperty)
            {
                return GetPropertyValue();
            }
            // Resolve a named extension method of DateTime, like "LastOfMonth"
            if (this.IsExtensionMethod)
            {
                return GetExtensionMethodValue();
            }
            // Parse a relative date
            if (this.IsRelativeValue)
            {
                return GetRelativeValue();
            }
            // Parse an absolute date
            return GetAbsoluteValue();
        }
        private bool IsProperty
            => typeof(DateTime).GetProperties()
                .Select(p => p.Name).Contains(this.DefaultValue);
        private bool IsExtensionMethod
            => typeof(DefaultDateTimeValueAttribute).Assembly
                .GetType(typeof(DefaultDateTimeExtensions).FullName)
                .GetMethods()
                .Where(m => m.IsDefined(typeof(ExtensionAttribute), false))
                .Select(p => p.Name).Contains(this.DefaultValue);
        private bool IsRelativeValue
            => this.DefaultValue.Contains(":");
        private DateTime GetPropertyValue()
        {
            var instance = Activator.CreateInstance<DateTime>();
            var value = (DateTime)instance.GetType()
                .GetProperty(this.DefaultValue)
                .GetValue(instance);
            return value;
        }
        private DateTime GetExtensionMethodValue()
        {
            var instance = Activator.CreateInstance<DateTime>();
            var value = (DateTime)typeof(DefaultDateTimeValueAttribute).Assembly
                .GetType(typeof(DefaultDateTimeExtensions).FullName)
                .GetMethod(this.DefaultValue)
                .Invoke(instance, new object[] { DateTime.Now });
            return value;
        }
        private DateTime GetRelativeValue()
        {
            TimeSpan timeSpan;
            if (!TimeSpan.TryParse(this.DefaultValue, out timeSpan))
            {
                return default(DateTime);
            }
            return DateTime.Now.Add(timeSpan);
        }
        private DateTime GetAbsoluteValue()
        {
            DateTime value;
            if (!DateTime.TryParse(this.DefaultValue, out value))
            {
                return default(DateTime);
            }
            return value;
        }
    }
}
DefaultDateTimeExtensions.cs
using System;
namespace Custom.Extensions
{
    /// <summary>
    /// Inspired from https://code.msdn.microsoft.com/A-flexible-Default-Value-11c2db19. See usage for more information.
    /// </summary>
    public static class DefaultDateTimeExtensions
    {
        public static DateTime FirstOfYear(this DateTime dateTime)
            => new DateTime(dateTime.Year, 1, 1, dateTime.Hour, dateTime.Minute, dateTime.Second, dateTime.Millisecond);
        public static DateTime LastOfYear(this DateTime dateTime)
            => new DateTime(dateTime.Year, 12, 31, dateTime.Hour, dateTime.Minute, dateTime.Second, dateTime.Millisecond);
        public static DateTime FirstOfMonth(this DateTime dateTime)
            => new DateTime(dateTime.Year, dateTime.Month, 1, dateTime.Hour, dateTime.Minute, dateTime.Second, dateTime.Millisecond);
        public static DateTime LastOfMonth(this DateTime dateTime)
            => new DateTime(dateTime.Year, dateTime.Month, DateTime.DaysInMonth(dateTime.Year, dateTime.Month), dateTime.Hour, dateTime.Minute, dateTime.Second, dateTime.Millisecond);
    }
}
And use DefaultDateTimeValue as an attribute to your properties. Value to input to your validation attribute are things like "Now", which will be rendered at run time from a DateTime instance created with an Activator. The source code is inspired from this thread: https://code.msdn.microsoft.com/A-flexible-Default-Value-11c2db19. I changed it to make my class inherit with DefaultValueAttribute instead of a ValidationAttribute.