Can I report early if my orders state "report date: NLT date "?

You can report up to 30 days early, but your DA31 must cover you to your report date.
If you're coming from OCONUS, there are DEROS rules that apply to when you can leave as well

So, NLT meaning "not later than"... Whenever your departing command wants to release you, you could report in to your new unit the next day if you wanted. If this is currently not the case in the Army then the Army needs to stop using NLT on it's orders.

These are the questions you should be asking S1 when you are getting your orders and going through the checkout process. If you leave a unit and originally planned to take 30 days leave but want to cut it short and show up before your NLT that is fine. If you just want to use travel days and save your leave entirely that's possible too but you should be coordinating this with S1