Unfortunately, no, the groups are not "pages". They may be displayed as a page but in reality they are groups of elements in a form. So there is no such thing as https://myLimeSurveys/index.php?group=2 .
The closest you could come to that would be to use JavaScript to advance the form
Code:
document.limesurvey.move.value = '2';
document.limesurvey.submit();
but as far as I know, that will only work if the group has already been visited.
I don't understand the problem with using a question and conditions to display the appropriate group. It doesn't matter if the questions are mandatory (except the group selection question).