Provided are methods of producing nucleic acid libraries. The methods include combining single-stranded nucleic acid binding protein-bound single-stranded nucleic acid (SSB-bound ssNA), an adapter oligonucleotide, and a splint oligonucleotide, to form complexes including the splint oligonucleotide hybridized to a terminal region of the SSB-bound ssNA and to the adapter oligonucleotide. An end of the first adapter oligonucleotide is adjacent to an end of the first terminal region of the SSB-bound ssNA, and the methods may further include covalently linking the adjacent ends. Also provided are compositions and kits that find use, e.g., in practicing the methods of the present disclosure.