Kali does not recognize my SSD at all | It sees only USB

Hello everyone. I am trying to install Kali Linux (64 bit) ver 2017.3 on a Dell XPS 13 9360 (64 bit), alongside with Windows 10 (64bit) on my C: drive. I got a UEFI boot mode enabled in BIOS and I am trying to install Kali from a bootable USB. In order to run the USB, I had to disable the Secure Boot option in my BIOS.

To create the FAT32 USB, I used the Win32 Disk Imager and a valid .iso file from the official site.

I also created enough unallocated space on the SSD, see this image: Attachment 2913.

The problem:

When I run the graphical installation from the bootable usb, I can proceed up to the point where I have to manage paritions. I select Manual creation of parition, yet only my Bootable USB shows as available, no SSD disk detected, nothing, similarly as in this picture from this thread.

Things I tried to do (and did not help):

• Reformat the unallocated space to ext4
• Run installation with Secure Boot on
• Force and not force the UEFI installation (this step)

Things that might be relevant:
At the beginning of the installation, I am getting this firmware files missing warning - Attachment 2914.

I would appreciate any help or guide, I searched several forums on the Internet, many of them just don't seem to me to be related to this issue. Thanks.