We present a rapid and efficient method to generate a family of platinum supramolecular square complexes, including previously inaccessible targets, through the use of ball milling mechanochemistry. This one-pot, two-step process occurs in minutes and enables the synthesis of the squares [Pt4(en)4(N∩N)4][CF3SO3]8 (en= ethylenediamine, N∩N = 4,4'-bipyridine derivatives) from commercially available precursor K2PtCl4 in good to excellent yields. In contrast, solution-based assembly requires heating the reagents for weeks and gives lower yields. Mechanistic investigations into this remarkable rate acceleration revealed that solution-based assembly (refluxing for days) results in the formation of large oligomeric side-products that are difficult to break down into the desired squares. On the other hand, ball milling in the solid state is rapid and appears to involve smaller intermediates. We examined the binding of the new supramolecular squares to guanine quadruplexes, including oncogene and telomere-associated DNA and RNA sequences. Sub-micromolar binding affinities were obtained by fluorescence displacement assays (FID) and isothermal titration calorimetry (ITC), with binding preference to telomere RNA (TERRA) sequences. ITC showed a 1:1 binding stoichiometry of the metallosquare to TERRA, while the stoichiometry was more complex for telomeric quadruplex DNA and a double-stranded DNA control.