You cannot even cast a spell without choosing a legal target for each instance of the word "Target" in the spell.
601.2c The player announces their choice of an appropriate player, object, or zone for each target the spell requires.
So if there are no creatures on the battlefield, you cannot cast it. You could target an opponent's creature, or a creature that does not have summoning sickness.
However, you can cast a spell even if part of it will not do anything. For example, you can cast Dredge even if you do not control any creatures or lands to sacrifice (assuming you have some way to get mana without creatures or lands). Dredge would resolve like normal, and you would follow the steps, ignoring those that are impossible. So you would fail to sacrifice anything, then you would draw a card.
- Resolving Spells and Abilities
608.2c The controller of the spell or ability follows its instructions in the order written.
609.3. If an effect attempts to do something impossible, it does only as much as possible.
But if a card uses the word "target", like Expedite, then it will not resolve unless it still has at least 1 legal target. So if you cast Expedite, and target a creature, but then someone responds by casting Boomerang to return that creature to your hand, then Expedite will never resolve, and you will not draw a card.
608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process. If all its targets, for every instance of the word “target,” are now illegal, the spell or ability doesn’t resolve. It’s removed from the stack and, if it’s a spell, put into its owner’s graveyard.