Task return type gives not all code paths return a value

returning Task.CompletedTask is cleaner.

public Task CreateAsync(ApplicationUser user)
{
  if (user == null)
  {
     throw new ArgumentNullException("user");
  }

   Task.Factory.StartNew(() => { Console.WriteLine("Hello Task library!"); }); 
   // other operations

   return Task.CompletedTask;
 }

Needs a return :

 return Task.Factory.StartNew(() => { Console.WriteLine("Hello Task library!"); });

Or better:

return Task.Run(() => { Console.WriteLine("Hello Task library!"); });

The parameter Task in the name of your method denotes the return value of this method.

Therefore the compiler expects at a certain point your method a return statement where you return an object of that type that you denoted in the name.

public Task CreateAsync(ApplicationUser user)
{

     if (user == null)
     {
         // this part of code will return from the method with an exception
         throw new ArgumentNullException("user");
     }

     // but this part of code is also expected to return something
     return Task.Run(() => { Console.WriteLine("Hello Task library!"); });

}