Run a view's bulk operation immediately but in background. Is that possible? Is it possible to run a view's bulk operation immediately after pressing the button but in the background (in other words, without forcing the user to wait until the progress bar completes to 100%)?

I understand that this can be achieved by enqueuing the operation. But the problem of this solution is that execution is postponed until cron is run.

Thanks.
PHP needs something to drive the process, it's not multi-threaded. Drupal's queue process runs by either the client's browser making a series of calls (kind of like it emulates the cron), or by the cron itself. 

Why isn't the cron an acceptable method? You can use something like ultimate_cron The control the schedule for each cron tasks.

Update

As @Molot mentioned, the CLI is an option. I believe shell_exec is subject to PHP's timeout (I could be wrong). See this blog post on executing PHP in an asynchronous fashion.