I got a good MSDN help: Embedding SQL Server Express into Custom Applications
It introduces methods to deploy by a class wrapper. (Usually, we create a setup project and add SQL Express as prerequisite to deploy)
And it also gives an idea to embed *.sql script as text resource and then read, execute the commands one by one:

private SqlConnection sqlCon = new SqlConnection();
private SqlCommand sqlCmd = new SqlCommand(); 
public string[] ParseScriptToCommands(string strScript)
        {
            string[] commands;
            commands = Regex.Split(strScript, "GO\r\n", RegexOptions.IgnoreCase);
            return commands;
        }

public bool RunScript(string strFile)
        {
            string[] strCommands;
            strCommands = ParseScriptToCommands(strFile);
            try
            {
                if (sqlCon.State != ConnectionState.Open) sqlCon.Open();
                
                sqlCmd.Connection = sqlCon;

                foreach (string strCmd in strCommands)
                {
                    if (strCmd.Length > 0)
                    {
                        sqlCmd.CommandText = strCmd;
                        sqlCmd.ExecuteNonQuery();
                    }
                }
            }
            catch (SqlException sql_ex)
            {
                MessageBox.Show(sql_ex.Number.ToString() + " " + 
sql_ex.Message.ToString());
                return false;
            }

            return true;
        }
Additional resource: Deploy SQL Server databases easily with an Installer class