Hi there SirPlerple,

unfortunately that isn't possible.

It would be pretty cool if it was, but there's some pretty complex issues in the way, including:

• Wizards of the Coast produced the books that you bought (from a bookshop or online retailer), whereas D&D Beyond is produced by Curse, who are one of several businesses that have licensed the 5th edition D&D rules off Wizards of the Coast. To allow proof of a physical book purchase to grant access on D&D Beyond, Wizards of the Coast would need to grant that same access to you for Roll20 & Fantasy Grounds (and any other companies that license the rules). This would likely cost Wizards of the Coast more than they received for the book, ultimately meaning they would need to charge around $100 per book to make this work.
• There is no reasonable way of providing proof that you own the book, further what happens if the physical book is sold on? The physical book was sold "as is" rather than promising access to any online tools that would be developed.

It's a complicated issue and one that has been discussed at length on these forums.

The staff team do understand that budget can be an issue for people though, so there's a pretty cool way of making small purchases.

Say you want to play a Forest Gnome Wizard, you can head over to the Marketplace page for the Player's Handbook and purchase the Forest Gnome subrace from there for just $1.99

The cool thing about this is, if you should decide to purchase the full Player's Handbook at any time during the future, the cost is reduced by any purchases you've made from that book, so you're not out-of-pocket for having made partial purchases along the way.

I have merged the two threads you made on this subject - please don't post the same discussion multiple times. :)