I had a similar issue. For me, switching from Chrome to Edge In Private did the trick.
"Best Move Challenge" frozen

Where do you find the best move challenge?
Click https://www.chess.com/best-move-challenge or search in Announcements

I had a similar issue. For me, switching from Chrome to Edge In Private did the trick.
My browser gave me a "404 Page not found" error when I tried to do a private window so I'll try it on another browser, I guess.
So we can't go to best move challenge in chess.com menu? Do I have to enter the link, or are there other ways to go to best move challenge??

I tried two other browsers and I have the same issue (Edge and Google Chrome).
Did you InPrivate & Incognito modes, respectively?

I tried two other browsers and I have the same issue (Edge and Google Chrome).
Did you InPrivate & Incognito modes, respectively?
Yes, this is what it looks like in Opera:
And this is what it looks like in Edge:
Same issue, same behavior.

Sorry, mate! I hope it gets fixed soon!
If I go into the HTML for the "Play" button, I see:
OK, so I change "disabled" to "enabled", and I change "not-allowed" to "allowed" and...
and...
ta-da! The "play" button illuminates and my mouse cursor looks normal again. Unfortunately, the play button still doesn't respond. But that does tell me that the issue is on chess.com's end.
Overview: I cannot click "Play" on "Best Move Challenge". The "Play" button is greyed out and the cursor converts to a "do not enter" sign. I refresh the page, same result -- I can't continue past this point.
Environment:
Browser: Brave 1.81.135 (Official Build) (64-bit) Chromium 139.0.7258.127
Computer/Operation system:
Processor Intel(R) Celeron(R) N4020 CPU @ 1.10GHz 1.10 GHz
Installed RAM 4.00 GB (3.82 GB usable)
System type 64-bit operating system, x64-based processor
Edition Windows 11 Home
Version 23H2
Installed on 10/6/2022
OS build 22631.5472
Experience Windows Feature Experience Pack 1000.22700.1106.0
Username: Sargon_Three
App links: https://www.chess.com/best-move-challenge
Expected Result: Game should continue with another reloaded board; cursor should not be a "Do not enter" sign