Maybe GraphComputation`ToGraphRepresentation can help?
IndexGraph[g1]; // AbsoluteTiming
IndexGraph @ GraphComputation`ToGraphRepresentation[g1, "Sparse"]; // AbsoluteTiming
{3.*10^-6, Null}
{0.002497, Null}
IndexGraph[g1]; // AbsoluteTiming
IndexGraph @ GraphComputation`ToGraphRepresentation[g1, "Sparse"]; // AbsoluteTiming
{3.*10^-6, Null}
{0.002497, Null}