Evidently, there was an extensive Belarusian partisan force opposing Nazi occupation (apparently involving as many as 153,700 partisans). The Wikipedia article I link to mentions that one of the major factors for the Soviet Union organizing this in Belarus in particular was its geography:
The Soviet authorities considered Belarus to be of the utmost importance to the development of the Soviet partisan war from the very beginning. The main factors were its geography, with many dense forests and swamps, and its strategic position on the communications going from West to Moscow.
This is likely why the poem mentions "deep forest glades" - Belarus was selected specifically for the existence of these forests.
Several authors (including Ales Adamovich, a relatively well-known Belarusian author) were involved in this war; while I haven't been able to verify whether Anatol Astrejka was personally involved, the author was highly likely to either have known someone who was involved in the Resistance or to have been personally involved in it.