在 in front of the nouns like tomorrow or exact dates and time
Yes, you can put 在 in your examples. And...

Pay attention to words like today/tomorrow, you can only add 在 when the time goes as a noun rather an adverb.
希望就在明天
明天会更美好: do not put 在 before.

In particular, for the first example, 在 must be added, check the differences below.
早在八月...: since August.
早八月...: error.
（在）八月初...:  in early August.