You can deploy a whole new build in a different directory, set it all up while the old build is active, then switch over once the build is complete. The easiest way to do it is using symlinks:
/project
/current (symlink pointing to /project/releases/build1)
/releases
/build1
/build2
ln -s /project/releases/build2 /project/current
If the webserver reads from /project/current, it doesn't know there's any change
If there is a disastrous bug in the new build, you can rollback to the old build by changing the symlink back again.
To ask (or google) your question better, you should be using words like "downtime", e.g. this is a "zero downtime deployment strategy". Naming your question as "Vite manifest not found during production build" is completely misleading.