Howdy, Nathan. Chrome user data resides in %LocalAppData%\Google\Chrome\User Data. Often the case when Chrome crashes on launch is to go into that folder and delete all files and folders within it (with care to backup the bookmark file). This is often the result of extensions.
However, in your case, since you just installed Chrome but it is failing to launch, the user data folder has not had a chance to build, which explains why it is likely non-existent.
To troubleshoot why Chrome is crashing, try the following first:
Open the Windows Event Viewer > go to Windows Logs > Application.
Look for any error that correspond to the time that the application crashed. Feel free to post them in image format or copy-paste text into a reply.
Additionally, if the Events are benign or non-existent, then you can enable what are known as user-mode dumps. This will dump the running instance of a crashing program into a dump file which can then be examined by a Windows debug program. To enable user-mode dumps, you will need to modify the registry and restart the computer and reproduce the issue. See this guide on how to set this up (applies to Windows 10 as well): https://windowsexplored.com/2010/08/11/enable-p...
You can then post one of these dumps and I can take a look at it.