Density and hardness of glasses are known to increase upon both compression at the glass transition temperature (Tg) and ambient pressure sub-Tg annealing. However, a serial combination of the two methods does not result in higher density and hardness, since the effect of compression is countered by subsequent annealing and vice versa. In this study, we circumvent this by introducing a novel treatment protocol that enables the preparation of high-density, high-hardness bulk aluminosilicate glasses. This is done by first compressing a sodium-magnesium aluminosilicate glass at 1 GPa at Tg, followed by sub-Tg annealing in-situ at 1 GPa. Through density, hardness, and heat capacity measurements, we demonstrate that the effects of hot compression and sub-Tg annealing can be combined to access a "forbidden glass" regime that is inaccessible through thermal history or pressure history variation alone. We also study the relaxation behavior of the densified samples during subsequent ambient pressure sub-Tg annealing. Density and hardness are found to relax and approach their ambient condition values upon annealing, but the difference in relaxation time of density and hardness, which is usually observed for hot compressed glasses, vanishes for samples previously subjected to high-pressure sub-Tg annealing. This confirms the unique configurational state of these glasses.