The other option is to file a $0 return via paper for back years or file a return reporting $1 of interest income to e-file. I’d do $1 of interest to efile, but either works if you want to file.
Yes, I know it’s not required, but it’s free, there’s no harm in it, and if you e-file the transcripts will process very quickly so you can upload them as proof of filing.
My opinion is that there’s really not a good reason not to file a tax return even if it’s just a return saying you had no income. Prevents others from using your SSN to file a return (it happens), if there’s a stimulus/other government benefit, it’s easier to get usually if you’ve filed a return, and in this case, easier to show the Department of State that you filed a return than explain to them why you don’t need to.
Again, not required, but seems to be the easiest solution here.