The two-dimensional electron gas occurring between the band insulators SrTiO$_3$ and LaAlO$_3$ continues to attract considerable interest, due to the possibility of dynamic control over the carrier density, and the ensuing phenomena such as magnetism and superconductivity. The formation of this conducting interface is sensitive to the growth conditions, but despite numerous investigations, there are still questions about the details of the physics involved. In particular, not much is known about the electronic structure of the growing LaAlO$_3$ layer at the growth temperature (around 800 $^o$C) in oxygen (pressure around $5times 10^{-5}$ mbar), since analysis techniques at these conditions are not readily available. We developed a pulsed laser deposition system inside a low-energy electron microscope in order to study this issue. The setup allows for layer-by-layer growth control and in-situ measurements of the angle-dependent electron reflection intensity, which can be used as a fingerprint of the electronic structure of the surface layers during growth. By using different substrate terminations and growth conditions we observe two families of reflectivity maps, which we can connect either to samples with an AlO$_2$-rich surface and a conducting interface; or to samples with a LaO-rich surface and an insulating interface. Our observations emphasize that substrate termination and stoichiometry determine the electronic structure of the growing layer, and thereby the conductance of the interface.
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