Final answer:
It is unlikely that this question refers to a factual event in classical music history, as none of the listed composers, Mozart, Beethoven, Haydn, or Handel, are known for singing mythological creatures into existence. The question might be metaphorical or fictional in nature. Referencing Strauss and Wagner, who composed music with mythological themes, could provide a hypothetical answer, although they are not options in the question.
Step-by-step explanation:
The question "Who sang the Dragons, Titans, and Giants into existence?" might not refer to an actual event but instead alludes to the creation of a mythological or fictional world through music compositions or operatic works by classical composers. Although none of the options provided, Mozart, Beethoven, Haydn, and Handel specifically, are known for singing such beings into existence literally, their music has indeed given life to various mythological and powerful narratives.
However, since the question does not align with known facts about these composers or their works, it is likely metaphorical or sourced from a specific fictional context—not documented historical information from classical music. We can mention that composers like Richard Strauss and Richard Wagner, who are not listed in the question, were known for their epic and dramatic compositions that often involved mythology and could hypothetically 'sing' such creatures into existence within their operas and tone poems.
Thus Spake Zarathustra by Strauss, as mentioned in the reference, is a tone poem that has a dramatic and powerful character, which could metaphorically give rise to mythic beings. Likewise, Wagner's operas like the Ring Cycle do delve into the world of gods and mythical creatures. But it's imperative to note that neither of these composers is mentioned in the list provided in the question, which makes it difficult to provide a direct and accurate response.