October 2021 PSAT scores will be released to students by the College Board on December 6th and 7th, 2021, depending on where you live in the US.
However, you can bypass this restriction by using a VPN (Virtual Private Network) to fool the College Board website into thinking you are in a different location, thus allowing you to view your scores on 12/6, no matter where you live.
Most reputable VPNs require paid monthly subscriptions, but many also offer free trials.
Despite their popularity, my strong suggestion is to avoid gimmicky (and possibly scammy!) "early scores" websites such as earlyscores.com—which offer the same service—as these websites require you to share your personal information and College Board account password, which should be kept confidential.
If you do use one of these websites, then I would urge you to change your password immediately afterwards, to prevent unwanted intrusions into your College Board account.
By the way, it is also true that educators will have access to your scores through the College Board's K-12 portal as early as November 29th, and that students whose schools use programs such as Naviance or Scoir might be able to access their scores early as well.