PC community seems to be suffering from the widest range of crashes among the three platforms, with two issues being the primary offenders lately - crash on launch and bad_module_info error. These two walkarounds worked for some players.
We will start with crash on launch, as this issue seemingly has a simpler walkaround. The problem here seems to be instigated by Easy Anti Cheat, but Origin's overlay also tends to crash the game as it is starting up. First, you will need to open Origin without launching Apex Legends.
After that, find Apex Legends in My Games Library, right-click the game and go to Game Properties. This window should show you whether you have Origin enabled in game. If it is enabled, like it's shown in the picture below, uncheck the option and click Save. The walkaround is fairly simple and it has worked for several players so far, although it is not guaranteed to work every time.
Bad module info error will take a little more effort though. First, you will need to navigate to the installation folder. The easiest way to do this is right-clicking the desktop icon - > Properties -> Open File Location. Once the folder is open, you will need to find r5apex.exe, which will likely be already highlighted.
Right-click r5apex and click Properties. Navigate to the Compatibility tab and find the Disable Fullscreen Optimisation option. Check the box next to it, save and exit. The next time you launch Apex Legends it might run in windowed mode, but you should be able to safely change to fullscreen in Apex Legends' in-game options.
We didn't test the fix to bad module error ourselves as we were lucky enough not to run into this particular issue, but the fix was found by a player who worked together with EA support in order to find a way around the issue. It is apparently a texture that keeps causing the problem.