To achieve laser direct welding of glass and metal without optical contact is hard, owing to the large difference in thermal expansion and thermal conductivity between glass and metal and an insignificant melting area. In this study, the high-power picosecond pulsed laser was selected to successfully weld the aluminosilicate glass/6061 aluminum alloy with a gap of 35 ± 5 μm between glass and metal. The results show that the molten glass and metal diffuse and mix at the interface. No defects such as microcracks or holes are observed in the diffusion mixing zone. Due to the relatively large gap, the glass collapsed after melting and caulking, resulting in an approximately arc-shaped microcrack between modified glass and unmodified glass or weakly modified glass. The shape of the glass modification zone and thermal accumulation are influenced by the single-pulse energy and linear energy density of the picosecond laser during welding, resulting in variations in the number and size of defects and the shape of the glass modification zone. By reasonably tuning the two factors, the shear strength of the joint reaches 15.98 MPa. The diffusion and mixing at the interface and the mechanical interlocking effect of the glass modification zone are the main reasons for achieving a high shear strength of the joint. This study will provide reference and new ideas for the laser transmission welding of glass and metal in the non-optical contact conditions.