I seem to be experiencing the same issue as described here https://community.kinsta.com/t/deployment-failed-no-log-no-deployment-time/2730. I am attempting to deploy two different static sites but both of them seem to just timeout with no feedback. Log entries just say There are no log entries. under the heading Build and rollout failed. Any help would be greatly appreciated.
I’m the OP and Kinsta was able to resolve the issue last week. I’m currently experiencing the same issue as you now.
Kinsta says their engineers are currently working on the issue, see link below along with current status
Update - We are continuing to investigate this issue.
Nov 27, 2023 - 21:26 UTC
Investigating - Our Engineers are investigating reports of deployment issues surrounding Static Sites. The issues are being observed as failed deployments lacking build logs.
We are working on restoring normal service as quickly as possible.
Nov 27, 2023 - 20:27 UTC
Hi @jpgrusling_fusionary and welcome to Kinsta Community!
Thank you @holatena 
That’s right, we do have the status page for this current Static Site issue that can be seen there .
It is still being checked and investigated by our internal engineers team, and we will keep updating that status page with the progress - please be patient, and hopefully this can be resolved as soon as possible.
Best regards,
Agus
Just an update that our internal engineers team has just deployed a fix for this case! Also that status has just been updated now (marked as Resolved!) 
Please kindly try to deploy your static site(s) again and see if everything is working properly as expected!
Best regards,
Agus