According to this Addgene blog:
There are four different HDR pathways to repair DSBs. Here are three
central steps of the HDR pathways:
The 5’-ended DNA strand is resected at the break to create a 3’ overhang. This will serve as both a substrate for proteins required for strand invasion and a primer for DNA repair synthesis.
Essentially, this resection process generates the required overhangs through partial degradation of one of the strands.
To understand the mechanism of resection a bit better, this is a good read:
Huertas, Pablo. "DNA resection in eukaryotes: deciding how to fix the break." Nature structural & molecular biology 17.1 (2010): 11-16.