string line = @"CONNECTION.TEST ""the connections is confirmed""";
int ndx = Array.FindIndex(line.ToCharArray(), ch => char.IsWhiteSpace(ch));
string line1 = line.Substring(0, ndx);
string line2BySubString = line.Substring(ndx).TrimStart();
string line2ByRemove = line.Remove(0,ndx).TrimStart();
Some discussion here of various techniques for finding the first index of a specific character in a string: [
^]