Lol how does one know that hey I'm this Class and gets a feel of their abilities?
The Adventurer Class knowledge will be laid out properly when the party find an Adventurers Guildhouse and scan their crystals. By way of the Gift of the Crystal, they will also get access to a magical emailing service too known as Source Comm, aswell as access to the Contract Network. It's kind of a mix of Source magic plus technology.
As far reasoning regarding dicovering skills and abilities @Zool's explaination is as good as any other. The Source crystal in each adventurers hand links them to The Wellsprings, which connects them with Source; the energy that makes up all of existence. It would make sense somewhat that they could dig deep and figure out their powers through instinct.
@Zapdos has cleverly set up discovery of Adam's abilities in advance of the fighting. If your powers/character are more methodical and cerebral, I would suggest taking his posts as an example of how to figure things out.
Arthur is... unique lol, I'll just say that. @Goblinguy's set up is a lot different from anyone elses.
@Teyao posts of James' discoveries was a mix of instinct and accident, then logical processing. Maybe try something like that?
There's a lot you can do, it just takes imagination and stretching of the rules. I know you'll do just fine.
Also, I would accept 'Isekai magic' as an answer lol