Under ultra-high vacuum, surface synthesis of 2D conjugated metal-organic frameworks (MOFs) was carried out through molecular beam epitaxy (MBE) growth to address the challenge of traditional solvothermal methods in achieving large-scale, defect-free single-crystal synthesis. Here, we chose an iconic 2D conjugated MOF, Cu₃(HOTP)₂ (HOTP represents the deprotonated derivative of 2,3,6,7,10,11-hexahydroxytriphenylene), as a case study to investigate the diversified self-assembly of Cu atoms and HHTP ligands, as well as the synthesis mechanism of the MOF fragment on the surface with and without O₂ annealing conditions by scanning tunneling microscopy. The results show that dumbbell-shaped [Cu(HOTP)₂] complexes, the target fragment of MOFs, can be successfully generated in an O₂ atmosphere, yet large-area extended MOFs remain elusive, highlighting oxidation and ligand deprotonation as two key factors that hinder the on-surface synthesis of Cu₃(HOTP)₂.