Let's think through an example.
There are seven "stacks", four discard piles, and the turning pile. I'll assume Texas-style drawing where you draw three cards at a time from the turning pile.
If the top of the stacks are:
black 2, black 3, black 4, etc, upto black 8
then there are no legal moves immediately. You can't pile black on top of black.
Of course this is true if they were all red cards, or any combinations of cards like black 2 black 2 black 3 black 5 black 9 black jack black jack.
There are also combinations possible of black 2, red 4, red 5, black 8, etc... such that you can't move anything, but these get horribly complicated when you consider the turning pile.
When you're starting the game, you can turn over the turning pile upto 8 times (three cards at a time with 24 cards left in the pack after dealing). You require that those 8 turns don't reveal anything you can match.
So continuing the thought of having black 2 to black 8 on show. You could draw: black 2, black 9, black jack, black 3, black 7, black queen, black queen, black king... and that's it, you've failed.
So yes, it is eminently possible to deal a layout with no moves, and frankly there will be quite a few of them. In my example, you could have 2,3,4,5,6,7,8 all clubs, or 2,3,4,5,6,7,8 all spades, or 2,3,4,5,6,7,8 a mixture of clubs and spades, or 2,6,3,5,8,7,4 of clubs and spades dealt in any order... or all hearts... or all diamonds... etc etc etc.