I propose 2 variations of the implementation:
1 - If you don’t have google services, and most people who use delta chat don’t, because of privacy concerns, then do a background check of messages every 10 minutes instead of constantly running in the background, that’s what SimpleX does.
2 - Delta Chat developers will launch a free, public Gotify server - a free implementation of a push server with self-deploying server. The Gotify client is available in f-droid. It can be included in the Delta Chat build for the version released in f-droid, or offered to be downloaded at launch.