The injection of liquid fuel at supercritical pressures is a relevant topic in combustion, but usually overlooked. In the past, the wrong assumption whereby the liquid experiments a fast transition to a supercritical state was made, thus neglecting any role of two-phase interface dynamics in the early stages of the atomization process. However, recent studies have shown that local thermodynamic phase equilibrium and mixing between the involved species allow the coexistence of both phases in this pressure range. In this work, a Volume-of-Fluid method adapted to variable-density real fluids is used to solve the low-Mach-number governing equations coupled with a thermodynamic model based on the Soave-Redlich-Kwong equation of state. The mixing process, interface thermodynamics and early deformation of a cool liquid jet composed of n-decane surrounded by a hotter gas composed of oxygen at 150 bar are analyzed. Although heat conducts from the hotter gas into the liquid, net condensation can provide the proper local energy balance at high pressures. Then, vaporization and condensation may happen simultaneously at different interface locations. As pressure increases, liquid and gas mixtures become more alike in the vicinity of the interface. Thus, a combination of low surface tension force and gas-like liquid viscosities causes an early growth of surface instabilities. Early results indicate some similarity with high-Weber-number incompressible flows. The role of vortex dynamics on the interface deformation is analyzed by using the dynamical vortex identification method.