I can provide only a proof by contradiction that magic items function before they've been equipped for 24 hours.
Assumed for Contradiction: An item does not function without first being equipped for 24 hours.
Given: Belt of Giant Strength
Belt of giant strength implies that it has effects before 24 hours have passed, but does not explicitly state it grants the referenced temporary ability bonus.
Therefore, we can conclude one of two possibilities:
1) The item at no time grants the temporary ability score bonus provided for in the item description, per the assumption for contradiction.
2) The item grants the temporary ability score bonus that it provides for during the first 24 hours of its being worn.
Now this is where you get into some RaI territory, wherein we must suppose a designer would not introduce a rule which was never actualized in practice. This would lead us to reject the first outcome. If you do so, we arrive at a contradiction, which yields the conclusion that the negation of our assumption is true, which is:
An item does function without first being equipped for 24 hours.
Furthermore, if there is not a rule in the text stating that items must or must not be worn for some amount of time before taking effect, proving either assertion false directly will be difficult due to the lack of falsifiability inherent in such a system.