Do Collectible Card Games without shuffling exist?
Not sure how applicable it is, since it never had an actual physical card-based implementation (and ergo isn't strictly on-topic for this site), but Alteil was an online game based on CCG deck-building mechanics. While the original Japanese game still appears to be in active development, this answer is based on the English localization of it that has been defunct since 2017.

Decks are built of thirty cards, limited only by a maximum of three copies of any given card.  One card can be played each round, and this card is freely chosen from all available cards so there is no shuffling or randomization involved; the player has full access to his own deck.

(Again, this doesn't strictly meet your requirements of "letting the players arrange their decks beforehand" as there's no actual drawing involved &mdash; the player's "hand" is effectively his entire deck throughout the game &mdash; but it arguably does meet "so they know exactly which card they draw when" so I'll keep going...)

All the randomization that's not in the card selection is found in the actual card abilities themselves.  For example, whereas targetting is common in a typical CCG (at least the ones I've played), it's actually an exception in Alteil.  Most attacks &mdash; even the default attack action &mdash; only hit random units within range, but the player has no control over which units beyond ensuring the intended targets are "within range".  Targetted attacks do exist, but usually with a trade-off (e.g. higher cost or lower damage).  As such, gameplay itself is much more akin to a tactics game than most CCGs, with a higher emphasis on field layout and timing.

Detailed rules can still be found in the Wayback archive of Alteil's Rule Book; the fundamentals of game phases and stack resolution and card-text-trumps-everything are clearly in-line with existing deck-building games, even if the whole game is probably too complex to (enjoyably) play as a physical CCG.