I've gotten the latest development build of Dolphin (as of making this post) running on Windows 7.
I've had to make a tweaked QT6 replacement for Dolphin. Later QT6 versions also request api-ms-win-devices-config-l1-1-1.dll, which I've added to the attached zip. To run any QT6 build of Dolphin, the fix here is required.
Versions after 5.0-16709 request functions missing from Windows 7 (but are included in 8.0), they could probably be replaced with dummy functions (due to them being used to detect if the native x64 application is running on arm64 hardware), but I've found that VxKex works to satisfy the requirement.
Get VxKex from here: https://github.com/vxiiduu/VxKex/releases
To run Dolphin, there are three (or five versions) that you can go for
5.0-16380 or 5.0-16391:
These require no mods, just unzip Dolphin and run. 16380 is the last beta build with QT5, 16391 is the last development build with QT5.
https://dl-mirror.dolphin-emu.org/builds/dolphin-master-5.0-16380-x64.7z
https://dl.dolphin-emu.org/builds/67/df/dolphin-master-5.0-16391-x64.7z
5.0-16709:
This is the last development build to require just QT6 dll replacement. No VxKex needed.
https://dl.dolphin-emu.org/builds/a1/cf/dolphin-master-5.0-16709-x64.7z
5.0-16710 and later:
On top of needing QT6 dll replacement, these require VxKex to be installed and enabled for Dolphin.
Latest beta as of edit: https://dl.dolphin-emu.org/builds/40/56/dolphin-master-5.0-18498-x64.7z
Latest dev as of edit: https://dl.dolphin-emu.org/builds/c4/49/dolphin-master-5.0-19266-x64.7z
Screenshot is outdated, but 19266 was tested and works.