Install Ubuntu to SSD On Ubuntu

I have a new SSD and I want to make a fresh installation of Ubuntu on it (so I can replace my existing SATA connected SSD on my computer).

Is there a way I could do that from my existing ubuntu computer? I am able to connect the SSD to the computer (via sata-to-USB cable).

I have installed VirtualBox and tried to "play with the settings", but I can't figure out if it's possible.

Yes, you can.

Use your existing operating system (on the SATA hard drive) to create a live USB of Ubuntu. Here is the official tutorial to create a live USB in Ubuntu.

Now, replace the hard drive with the SSD and boot with the live USB. Then, install Ubuntu from scratch into the SSD.