The One UI 2.0 Beta is only available on the Factory Unlocked models of the Note 10. Carrier versions will have to wait until the full release to get Android 10. (At least for US models anyways.)
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I dont think you will be able to get the beta since you got your phone through a carrier. If I am wrong, you check the notifications page in the samsung members app. You should see a banner allowing you to join the beta
The note 10/10+ One UI 2.0 beta is currently closed. I have 2 note 10+ and 2 S10+ on the beta....runs smoothly and absolutely no issues on either of the 4 phones
The beta spots for the Note 10 were probably filled a couple weeks ago. Once the enrollment period has ended, there's no official way to get the beta update.
A week ago I was seeing people on here saying they kept checking in now and then, and the banner would come up and they could register. I was thinking if someone opted out, that spot would be open for someone else