Learn Polish: Dzisiaj wcześnie rano jadę do przedszkola. - Today I am driving to kindergarten early in the morning.

This is because of the preposition do (to), which always forces the noun that follows it into the Genitive case. The dictionary form of the word is przedszkole (a neuter noun). To form the Genitive for neuter nouns ending in -e, we drop the -e and add -a, giving us do przedszkola.

Could I say idę instead of jadę in this sentence?

Only if you are walking! In Polish, idę strictly means going on foot, while jadę means going by some form of transport (like a car, bus, or bike). Since the sentence uses jadę, the speaker is definitely riding or driving to the kindergarten.

Is rano (morning) in a specific grammatical case here?

In this sentence, rano acts as a fixed adverb meaning 'in the morning,' so it doesn't change its ending. When paired with wcześnie (early), it forms the very common time expression wcześnie rano (early in the morning).

Why is the subject 'I' missing from the Polish sentence?

The verb jadę already means 'I am driving' because of its -ę ending. In Polish, it is standard to drop the pronoun ja (I) unless you want to add special emphasis, like pointing out that you are doing it rather than someone else.