Do you have a folder called C:\Users\your_username\Documents\STAR WARS Squadrons\settings ? The Steam version's config/save files are located at C:\Users\your_username\Documents\STAR WARS Squadrons Steam\settings, so if you can find the STAR WARS Squadrons\settings folder created by Origin, you might be able to copy BootOptions, ProfileOptions, ProfileOptions_profile, and ProfileOptions_profile_synced over to the STAR WARS Squadrons Steam\settings folder. I only have it on Steam, so I am not entirely sure if that's where the saves are stored for the Origin version. Additionally, even if you do copy em over, they might be encrypted. You'd be one of the first to test and find out, so be sure to report your findings in any event!
Be sure to back up your Squadrons Steam\settings folder contents before overwriting with the Origin files, just in case it doesn't work and you've already restarted on Steam!