There is a workaround, but it requires a wired connection and Secure Boot enabled to get started.
There is a bug in the
intel_lpss driver which causes booting to fail with Secure Boot disabled. This applies to both the installation media and the finished installation. In BIOS settings, you need Secure Boot enabled for the installation. We'll disable it later. However, you need to do the fixes described later so you can turn off Secure Boot, allowing WiFi drivers and other drivers to be installed.
If you're trying to dual boot, make sure you have Windows installed already and you shrunk the Windows partition to create free space for elementary. Otherwise, you can just go through the installer as normal.
The easy fix described on ArchWiki is to blacklist the
intel_lpss_pci module. However, it doesn't work with the Ubuntu-flavored kernel. You'll need a mainline kernel. And if you just blacklist the module, you'll lose support for touchscreen, 802.11ac WiFi, and other useful things.
The best fix is to recompile the Linux kernel with a patched
git clone https://github.com/torvalds/linux.git
git checkout v5.3 # or latest stable
git apply sqPv8ShP
The source of the patch is this Reddit thread.
Build the patched kernel using the second method in this answer. Then install the generated dpkg files. The compilation will take 30-120 minutes.
At this point you should be able to boot using your new kernel. In the GRUB menu, select "Advanced options for Elementary OS" and you should be able to see your new kernel and boot from it.
Verify your computer boots properly and if so, you probably want to set your new kernel to be the default. Follow this guide to do so.
You should also disable Secure Boot at this point.
The XPS uses a Killer AX1650 wireless chip. The drivers are not included in the installation by default. You can follow this guide to install them.
You already have the
linux-firmware repository from the last step, so
cp -r linux-firmware/intel/* /lib/firmware/intel
and reboot. Your WiFi and Bluetooth should be working now.
Open AppCenter and update to get the 5.1 update and drivers for various peripherals, including video acceleration. Reboot again and check out the new greeter.
Original instructions are on my blog. It's written for the 2-in-1 but it seems like it should work for the clamshell version too.