Probably not, especially since it sounds like you have already tried the first method, and like the second one does not apply here.
If the developer is not allowing downloads of older versions of their app, that casts doubt (in my mind) on whether the third method would have any chance of success. (And if you had a newer phone, why not just use it instead of using the old iPhone 7?)
MakeUseOf – 3 Ways to Install Older Versions of Apps on an Older iPhone
Summary
- Try to download the app in spite of its minimum iOS requirement – and hope that you get a "Download an older version of this app?" dialog instead of an error message.
- If you have previously purchased a compatible version of the app, try redownloading it from your purchases list (Redownload apps and games from Apple - Apple Support)
- If you have a newer, compatible device on the same Apple account, download the current app on that device … then try to re-download the app on your old device (crossing your fingers and hoping that it will give you an old version, instead of an error message)