1. Do I need some kind of particle in between or can I straight up say
”kino kouen de jogingu o shinakatta”
\[I didnt got jogging at the park the day before yesterday\]
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2. Is it ok to start a sentence with ”kyou” \[today\] or is it seen as unnecessary in the same way that ”watashi” is unnecessary?
3 comments
It’s fine to include today, it’s not the same kind of unnecessary repetition as watashi unless you’re adding it to every sentence or something
Relative times like today don’t use particles like に, tho they can use は to add some vagueness or contrast. Exact times that are absolute like Tuesday or 2pm or December 25 would all take に
In general, most adverbs (which temporal nouns like the ones you mention function like) may be placed almost anywhere in the sentence without particles. However, because many adverbs originated from nouns, they also occupy an interesting duality whereby they can also be used like nouns (even taking particles for nouns).
Based on this, both sentences you give are acceptable. You could also have prefaced 今日 with the topic particle if you so wished.
Adverbs for relative time don’t take a particle, except when being made the topic of a sentence.
今日、公園でジョギングをしなかった。I didn’t go jogging in the park today. (Statement of fact)
今日は公園でジョギングをしなかった。I didn’t go jogging in the park today (but implying that you went jogging on a different day, or will go jogging on another day).