We report that in unannealed LaAlO3/SrTiO3 (LAO/STO) heterostructures the critical thickness for the appearance of the two-dimensional electron gas can be less than 4 unit cell, the interface is conducting even for STO substrates with mixed terminations and the low-temperature resistance upturn in LAO/STO heterostructures with thick LAO layers strongly depends on laser fluence. Our experimental results provide fundamental insights into the different roles played by oxygen vacancies and polarization catastrophe in the two-dimensional electron gas in crystalline LAO/STO heterostructures.