This is caused by compiling shaders. To prove this out, install IncrediBuild (you don’t need a license for standalone mode and it can be added with the Visual Studio installer) then open your project. You will see the shaders being actively compiled. The splash screen may “freeze” at 39% but you can see the compilation occurring (and with IB it farms it out to all your cores instead of sequentially).
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Worked for me too 
I deleted the problematic project and created a new one with raytracing disabled. That fixed my issue hope it helps others. I don’t think my card supports raytracing.
go to your project folder on your drive and rename config folder to config_old, thats it… now open your project and its done…
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Please watch this Unable to start Unreal Engine, stuck at 39% ( SOLVED 100 % ) Unreal Editor initializing error - YouTube worked for me 100 % 
i made this video after solved problem
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He’s right! Just gotta be patient and let the shaders recompile:
I was upgrading Unreal. When Unreal asked for access to the internet I said NO. It was stuck at 39% overnight. Restarted Unreal, this time when it asked for access to the internet I said YES. Loaded in about a minute.
The same thing happened to me. I have a GTX 1080 Ti, which I heard could handle raytracing, it only worked when I turned it off though.
I have installed Unreal 4.26 and I have same problem, Unreal stuck initializing at 39%. I have tried Deleting/Renaming the Config folder which makes Unreal launch successfully but, when we need Planar reflections, SSR or Raytracing enabled, Unreal asks to restart and then it gets stuck again initializing at 39%.
These are my PC specs:
Intel i7 4790k
8GB DDR3 1866 MHz Ram
Zotac GTX 1060 6GB AMP
z97 Pro Gamer Mobo
With DXR enabled Windows version and latest Nvidia studio drivers. I hope realtime raytracing should work on GTX 1060.
Thank you!
It worked!
Woooooooorrrrrkkkkkk!!! Thank you, monster lord!
a lot! It worked
Dozens of complains about this issue and still not fixed.
Very, very frustrating and I´m very used to CGI softwares etc.
I also had this issue at first. I resolved it by disabling the ray tracing option of my project
a lot!!! That work for me bro.
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(IF YOU WANT TO ENABLE VIRTUAL TEXTURES 100% FIX) -Most of the fixes that people have provided on this forum just reverts your project settings to default allowing to you to open ue4 but not keep the project settings you have. This is not helpful if you are trying to enable Virtual textures in the project settings because it just deletes it after the revert. If you are getting this problem when enable virtual texture support try this - Open UE4 - Select a New Project (Game) - Select Third Person - (IMPORTANT) Select Raytracing Disabled and No Starter Content in Project Settings - Create the Project - Navigate to the project settings tab once the editor opens - Search and select Enable Virtual Texture Support - Click Restart now in the bottom right of your editor - Your editor will restart and sit at 39 % for atleast 3 mins but wait another 2 minutes and your editor will open - In the bottom left viewport of the editor it will say compiling shaders - don’t wait for it to finish just close the project and open the (Project you wanted the Virtual texture shaders on ) and enable virtual textures and select restart now and wait for the shaders to compile and it should work.
This worked for me too, but you can equally just delete the Config folder. When I made a new project, Unreal thought that I wanted my project to be VR for some reason, and it was a hiccup in SteamVR causing the stall at 39%.
Deleting the config appears to work around this as the engine reassigns a default config. To Everyone: If you aren’t building a vr app, I’d advise looking under Settings> Plugins above the main viewport and disabling the pre-installed VR plugins
For me it was also stuck at 39%. It worked by doing the following:
1 - Finish this locked project with the task manager
2 - Go to your project settings and DELETE the “Config” folder
3 - Start the project again by opening Unreal through the project that is next to this folder