Is it possible to install KVM in WSL 1?

No. KVM is a Linux kernel feature, and WSL1 doesn't have a Linux kernel; it imitates a Linux kernel, somewhat like Wine imitating the Windows environment. You cannot actually load Linux .ko modules into it.

This may be possible in WSL2 – in theory – as WSL2 runs a real Linux kernel and does so through Hyper-V, which supports "nested virtualization" if the CPU is also compatible, meaning that the WSL2 VM could itself run more VMs inside. However, I don't know if the standard Microsoft-provided Linux kernel _{(words you never thought you'd hear)} is compiled with KVM support, but at least they have instructions for compiling a custom kernel.

It might also be possible to somehow convince your libvirtd to run Qemu on Windows, as Qemu actually supports running VMs through the Windows Hypervisor Platform (which is the Windows equivalent of KVM), so you could run WSL2 and qemu.exe -accel whpx side-by-side without them conflicting.

(Of course, Qemu on Windows can also use the Intel HAXM hypervisor with -accel hax.)

(Perhaps WSL1 could implement the /dev/kvm API in terms of Windows Hypervisor Platform, but it doesn't do that, and I don't think it's going to receive any new features given that the focus in WSL2.)