The only way to get on the beta is to pre-order the game through Bethesda. The game is not being released on Steam either this time so it’s Bethesda.Net or nothing.
The Official beta FAQ states the following:
PC players who have already created an account and pre-ordered Fallout 76 on Bethesda.net can access the B.E.T.A. once it’s live via the Bethesda Launcher. If you haven’t already, you can download the Bethesda Launcher for free.
Console players who pre-ordered Fallout 76 digitally on console via the Xbox Store or PlayStation Store will automatically be able to access the B.E.T.A. once it’s live on their respective platforms. Please search for “Fallout 76 beta” once it’s available on your console’s store to download it.
If you pre-ordered Fallout 76 via participating physical or digital retailers, such as Amazon or GameStop, you will receive a code on or with your physical or digital receipt. PC players can simply redeem this code on the Bethesda Launcher to gain access to the B.E.T.A. once it’s available. However, if you play on console this code is not your actual B.E.T.A. code. To receive your B.E.T.A. code, please follow these steps: