Welcome to the community @Ihor-Fin.do!
I never worked with either of them. I would have expected that not matter what service you are working with to do that, they have an API which you can use with the HTTP Request node.
@Ihor-Fin.do Why not firebase?
Hey @Ihor-Fin.do, in addition to Firebase suggested by @mcnaveen n8n also has built-in support for Pushbullet and Pushover which might be a bit simpler to set up (if you only need such messages for yourself for example).
A self-hosted solution offering push notifications would be ntfy.sh, which can be used through the HTTP Request node as suggested by @jan.
Fwiw, I’ve used these all of the three services above at some point and they all worked well with n8n. There are probably more out there most likely also working fine 
Addition to @MutedJam suggested you can use Gotify as well.
There is now support for custom ntfy.sh servers with the ntfy node :