I know we do not need copyright registration to publish a book. But how about before publishing first if we apply to copyright office but then withdraw the application or it is closed without registration or even refused and we do not file again? We can still publish correct?
As gnasher729 says, you are not required to register your copyright in order to publish, but that's not the end of the story. In many jurisdictions, you are required to submit a few copies of your work to the national library of last resort when you publish it, regardless of whether you register a copyright (or take any other copyright-related action). This used to be associated with copyright registration, but that link was severed (in the vast majority of jurisdictions) with the Berne Convention and/or some implementing legislation passed around the same time (which made copyright fully automatic and removed many other formalities from the copyright process).
The Court of Appeals for the District of Columbia Circuit has held that this requirement is an unconstitutional taking, and may not be enforced, specifically because it is no longer associated with copyright registration (and can no longer be characterized as a voluntary exchange between the publisher and the government). Therefore, it is somewhat plausible that the US Congress will see fit to change this arrangement in the near future.
You are the copyright holder if you are the author, or your company is the copyright holder if you wrote the book as an employee. That is completely unrelated to registration. You can even create a book with all weather reports of the last ten years, which doesn't have any copyright because there is no creativity involved, and publish it. It would be quite boring so nobody will buy it, but you are free to publish it.
What copyright registration does is give you some evidence that you are the copyright holder, and some tool to make an infringer pay more damages if they copy your book without permission. But there is nothing stopping you from publishing the book without trying to register the copyright, with registration started but not finished, with registration abandoned, and so on.
If you abandon the registration I see no reason why you can't try again. You pay some fee every time. The copyright office will gladly take your fees ten times if you start registration, abandon, and repeat this ten times.
Starting the registration process may have the advantage that a possible infringer knows that you may have a registration soon, which makes copying legally riskier for them and that fact alone might stop them.