Related but not duplicate: Why did the Jedi take the clone army without further thought? and How does Obi-Wan reconcile the fact that the Separatists apparently commissioned the clone army for the Republic?
In Star Wars Episode II: Attack of the Clones we see Chancellor Palpatine had only just barely received his emergency powers and suddenly he already has a huge clone army big enough to rescue the Jedi and fight the Separatist army on Geonosis. If the Galactic Senate actually believed they were just now allowing Palpatine to create an army for the Republic, then weren't they a little suspicious when the existence of a pre-requested, fully grown, battle ready clone army is revealed very soon afterward?
Of course we know the Jedi were suspicious since Taun We claimed a Jedi ordered the army for the Republic and they know that's not true. However the Jedi don't do much about it. They even go on to serve as generals over the Clones in the war, knowing full well that someone had pre-ordered these clones without Senate or Jedi Council approval. They even learn the Sith ordered the Clone army but still they do nothing and tell no one.
MY QUESTION: Was anyone else suspicious of the sudden convenient appearance of a Clone army? I realize that initially they, like the Jedi, felt that there was no other choice than to use the Clone army at first but the Clone Wars lasted from 22 BBY to 19 BBY! Three years is a long time for the entire Republic to use and trust a conveniently pre-ordered army of unknown origin.
One would think that the sudden convenient appearance of a ready for battle clone army right after the Chancellor had only just gotten special permission from the Senate to have an army would tip people off to the possibility that the Chancellor was orchestrating the whole thing and had gone behind the Senate and Jedi Council's backs to pre-order this clone army for some ulterior motive. In the Clone Wars show we even see several groups lobbying for peace talks, negotiation, and cease fires etc. Why did none of those groups use the "We don't even know who ordered this Clone army!" argument as a way to at least call for a stop to the use of the Clone army?
Update: I'm accepting the answer that Tarkin was suspicious. However, feel free to answer whether anyone else was suspicious. Both Legends and canon answers are welcome.