Is it possible to connect the Google Maps API through reverse proxy in my app?

Your solution is a blatant violation of Google's terms and conditions.

10.1.1 (a) You must not access or use the Maps API(s) or any Content through any technology or means other than those provided in the Service, or through other explicitly authorized means Google may designate. For example, you must not access map tiles or imagery through interfaces or channels (including undocumented Google interfaces) other than the Maps API(s). https://developers.google.com/maps/terms

Legal issues aside, I think you answered your own question. "Google Maps API is not a necessity because there are replacements to it in our country".

But if your hell-bent on using Google Maps you can use their tiles with a 3rd party library like leaflet for web content. Native mobile apps are an entirely different problem though...one which I suspect is either a: not possible or b: not feasible.

FWIW, this doc from Google states it is acceptable to cache map images.

https://developers.google.com/maps/premium/optimize-web-services#cache

Significant correction to the accepted answer:

The cited section 10.1.1 no longer exists. Moreover, searching for the terms "authorized" or "other than" in the Terms & Conditions (T&C) returns no hits for a similarly worded replacement.

In conclusion, upon reading the T&C it appears that Google no longer explicitly says You must not access or use the Maps API(s) or any Content through any technology or means other than those provided in the Service nor does Google appear to provide a replacement.

T&C here: https://cloud.google.com/maps-platform/terms/