So my problem happen with EAC.
When I start without EAC the game start, I go on the main menu and can play the campaign but the game crash (with an Unreal Engine bug report) after I click on the skirmish/multiplayer button during the loading screen.

I know MP isn't activated without EAC but now i have game with only the campaing working

Edit : I looked up on the internet and found a way to launch the game without any issue. You have to go in the game file and launch the game with the .exe.
Launching the game with Galaxy seems to be the issue.

I have exatly the same problem, it's good to know I am not the only one with this issue :)
Strangely on Steam the problem doesn't occur. The game runs fine with EAC and battles/skirmishes are playable without EAC.

Two weeks later and I haven't heard anything from support.

Ok I managed to get it to work, I'm at the start of the first mission now, see included proof (It's not getting attached for some reason.).

Here's my research and my solution.

First the game gave me the XInput1_4.dll missing error. This was solved by going to the ".../Windows/System32" directory and copying XInput1_3.dll to the game directory. Renamed it there to XInput1_4.dll. Running the game then gave me a meaningless error. I installed the game on a Win8.1 machine where XInput1_4 was already available and there it gave me the XAudio2_9.dll missing error. I assumed this was the meaningless error on my Win7 machine.

Getting the XAudio2_9.dll is more complicated as you can't just do the same trick as above for XAudio2_7 (W7) or XAudio2_8 (W8.1). The good news is that Microsoft made a separate version of the dll compatible with windows 7 and windows 8.1. Google "Developer guide for redistributable version of XAudio 2.9" to find documentation. (I'm unable to post links for some reason.)

In short, you need to install the Microsoft.XAudio2.Redist package in Visual Studio, create a trivial project that uses the package and build it. In the build directory there will be an XAudio2_9Redist.dll somewhere, copy it to your game directory and rename it to XAudio2_9.dll.

After going through these steps the game finally started for me. (I've excluded some other steps which allowed the game to start but crash at main menu.) No idea how stable it will be though.

Perhaps GOG staff can take a look at this as well and gift me a game since I'm doing their job :^).

Wow, congratulations :) You should email Epic to let them know you have solved theirs problem with their U4 engine ;)

Hello everyone.
I'd like to put my two cents to the discussion.
When the game was in 1.0.8 version i had a problem starting it because of the missing XAudio2_9. Copying it manually from laptop with Windows 10 to the game folder gave warning about other missing files.
When game was updated to version 1.0.12 it seems, it was still missing XAudio2_9, but take these information with a grain of salts, because I updated game with GoG galaxy 2.0. I do not know how things are for offline installers. Anyway now coping XAudio2_8 from system32 to the game folder and renaming it to the XAudio2_9 seems to work, at least in my case.
I hope that information will help other customers.
Best regards
Mateuszy

I made an account here on GOG, just so I could tell you.

Thanks. It may be a little convoluted, but I did everything you said, and it finally f-ing worked. I had looked all over, and would definitely not have figured this out on my own, if I hadn't seen this solution.

Cheers, mate.

Np, I appreciate it.

Thanks bruh. This worked for me perfectly. You're da best.

Hey this was helpful. In an effort to get BFA running I uninstalled all visual studio and microsoft runtimes on my computer. I didn't want to go through the trouble of putting VS back on my computer and any future readers of this thread may not want to go through that trouble. You still gotta do a programmer-y thing to get it to work but this is what I did based of your findings.

1. I downloaded nuget.exe as instructed from Microsoft (I used the dist.nuget.org latest nuget.exe link there) and moved the exe file to my Desktop. Nuget is a package manager so it will allow you to download xaudio & 'dependencies'. You can delete this once completed.
2. Moved it to my Desktop for simplicity sake
3. Went to start menu and clicked the CLI Terminal 'Command Prompt' icon (you may need to search for this)
4. Once terminal was started I typed (ignore quotes) 'cd Desktop' (you may need to put the full path in to your desktop) & pressed enter showing a change of path to 'C:\Users\<My Username>\Desktop'
5. Found the nuget.org package page and looked 'Package Manager' instructions
6. Noted the instruction 'Install-Package Microsoft.XAudio2.Redist -Version 1.2.8' (we will ignore the first part) which informed me I would need the portion 'Microsoft.XAudio2.Redist -Version 1.2.8'
7. Went back to terminal and typed (ignore quotes) 'nuget.exe install Microsoft.XAudio2.Redist -Version 1.2.8' (if you are copy-pasting you'll need to right-click in terminal to paste) and pressed enter
8. Went to my Desktop and found 'Microsoft.XAudio2.Redist.1.2.8' which is a folder nuget downloaded
9. Within that folder I made my way to 'build\native\release\bin\x64\xaudio2_9redist.dll' & duplicated/copied and change the name to 'XAudio2_9.dll'. This file is 947 KB. Note: if you are not a 64-bit computer/OS you'll need the x86 version
10. Moved to 'C:\Windows\System32'
11. Ran BFA From Steam (sorry I'm a steam user). Since I had cleaned everything off my computer it took a good 5 minutes to start after the initial quicktime screens

I didn't want to download from those janky sites so I went this route. I definitely started with the Unreal Distribution Error; but after nuking anything Visual Studio C++ on my computer I just re-installed the latest Unreal Runtime & DirectX (cleared caches & reboot) I still had this one issue with the audio. I feel much better using this 947kb file over the old 247kb .. gives me a better sense that it'll work :P

TLDR;
Download nuget.exe from microsoft & move it where you can find it from terminal aka. Command Prompt
Open terminal (command prompt) and cd into the folder
Execute this command (without the quotes): 'nuget.exe install Microsoft.XAudio2.Redist -Version 1.2.8'
That'll provide the file you need Microsoft.XAudio2.Redist.1.2.8\build\native\release\bin\x64\xaudio2_9redist.dll (use x86 for non-64-bit)
Copy/Move that file to Windows\System32 and ensure its named XAudio2_9.dll
Play the game

The issue can also come from the CPU see the section about general troubleshooting
"Game does not launch - Intel 10th gen CPU or newer"

This worked for me