Q:

How to open PuTTY terminal directly, without configuration window?

When you open Putty,the configuration window is shown:

Is there any way, to directly open Terminal, without that welcome (configuration) window? Where I can start typing the codes directly, like: ssh user@example.com -p 80

A:

If you just want to skip PuTTY configuration/login window:
putty.exe user@host -P port

Or, to open your existing stored session:
putty.exe -load "stored session name"

If you are looking for a console SSH terminal, use Plink from PuTTY package.
It has the same command-line syntax as PuTTY and similar to OpenSSH ssh:
plink user@example.com -P port

(or again, you can use -load)

Or use OpenSSH ssh itself. There's now an official Microsoft build of OpenSSH for Windows.
On Windows 10 version 1803 or newer, you already have OpenSSH built-in. On older versions of Windows 10, it can be installed as an optional Windows feature. On older version of Windows, you can just extract the client-side tools from a .zip (latest release), no installation is need.

A:

You can always save the definitions, and in recent versions of Windows (assumed), you can open these from the start menu.  
Try Putty -load *savedentry*

A:

I see there's an accepted answer already, but if you're using Windows 10, the Windows Subsystem for Linux (WSL) is a great alternative.  You can put aliases in your .bashrc file, or you could reference the command history to reopen a previous connection.  You can also install tmux and have several connections open at once.

