Honestly, it's kinda wishy-washy. Buena Vista Street is out of the question, because although they are blazing through the contruction, the timeline is pretty strict. Cars Land MIGHT have a soft opening that early. You can use the soft-openings of Star Tours/Little Mermaid from last year to help:
Star Tours (the one that was done pretty early): May 20th Soft-Opened: that's 14 days before the attraction opened and it sounds pretty equal to the timeline of Cars Land.
Little Mermaid (brand-new ride): I saw cast members sneaking on and riding it on May 14th, but the actual soft-openings also started around May 20th as well-this will probably be closer to BVS.
Harry Potter (an entire land) in Orlando started soft-openings in early May to hotel guests only for a few hours in the morning to get the land to brace itself for the crowds. Hope this helps.