Ask your DM, only they can answer
Creating Adventures (DMG 71)
Creating adventures is one of the greatest rewards of being a Dungeon Master. [...] When you design an
adventure, you call the shots. You do things exactly the way you want
("You" in the above refers to the DM.)
A Clear Focus on the Present (DMG 71)
Instead of dealing with what happened in the past, an adventure should focus on describing the
present situation, what the bad guys are up to, and how the
adventurers became involved in the story.
(Emphasis mine in the above.)
How to Play (PHB 7)
- The DM describes the environment.
All the above rules are indirectly giving the answer to your question. It is up to the DM to decide how the adventure starts, including whether you've had a long rest and have gained any benefits from your class abilities.
Just ask them. Getting a technically correct answer from internet people will not sway them either way on whether you can have your portent dice at the start, or not, as they may decide that the opening scene begins with you exhausted and your resources drained.
Also, I have never seen any rule that explicitly states the exact conditions of how an adventure starts, in regards to resources, so you are unlikely to find any RAW source to tell you an answer one way or the other.