ASP.NET Core SQL Connection - Impersonate User

I am having trouble finding documentation on how to impersonate a user and open a SqlConnection as that user.

Background:
DBAs have provided an Active Directory account that has access to a database. When using the connection string:

"Server=server\instance;Initial Catalog=mtdatabase; User ID=domain\user; Password=mypassword;";

I get an error that the user is not allowed. When using Integrated Security, it ignores the specified Username and Password, and uses the currently logged in user (me when I am debugging locally).

How can I impersonate the user with the provided information in my code to ensure that it is used to open up the connection?

Currently, I am using the following code, which is failing when trying to open the connection:

[Route("api/[controller]")]
public class HomeController : Controller
{
    // GET: /<controller>/
    [HttpGet]
    public IEnumerable<string> Index()
    {
        string connString = "Server=server\\instance;Initial Catalog=mtdatabase; User ID=domain\\user; Password=mypassword;";

        using (var conn = new SqlConnection(connString))
        {
            conn.Open();
            conn.Close();
        }
        return new string[] { "value1", "value2" };
    }
}