Is it possible to generate Google App Invite server-side?

I am developing an Android App (along with API server) with plans to promote it via App Invites.

Currently I see how to create and send invite from installed app itself (using corresponding intent, which app user will turn into email or sms link).

But may I generate such a link separately, at my server-side? So that I register that link at Google API, and send it independently, so that it works just if it was generated in-app?

Yes, but what you're looking for is a Dynamic Link (the thing you probably care about for the app invite):

Android: https://domain/?link=your_deep_link&apn=package_name[&amv=minimum_version][&ad=1][&al=android_link][&afl=fallback_link]

iOS: https://domain/?link=your_link&ibi=bundle_id&ius=url_scheme[&ad=1][&ifl=fallback_link][&at=affiliate_token][&ct=campaign_text]

Read more here (Android): https://firebase.google.com/docs/dynamic-links/android#create-a-dynamic-link-in-the-firebase-console

and here (iOS): https://firebase.google.com/docs/dynamic-links/ios#create-a-dynamic-link-in-the-firebase-console