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The injection of liquid fuel at supercritical pressures is a relevant but overlooked topic in combustion. Typically, the role of two-phase dynamics is neglected under the assumption that the liquid rapidly transitions to a supercritical state. However, a transcritical domain exists where a sharp phase interface remains. This scenario is the common case in the early times of liquid fuel injection under real-engine conditions involving hydrocarbon fuels. Under such conditions, the dissolution of the oxidizer species into the liquid phase is accelerated due to local thermodynamic phase equilibrium (LTE) and vaporization or condensation can occur at multiple locations along the interface at the same time. Fluid properties vary under species and thermal mixing, with similar liquid and gas mixtures near the interface. As a result of the combination of low, varying surface-tension force and gas-like liquid viscosities, small surface instabilities develop early. The mixing process, interface thermodynamics, and early deformation of a cool liquid n-decane jet surrounded by a hotter moving gas initially composed of pure oxygen are analyzed at various ambient pressures and gas velocities. A two-phase, low-Mach-number flow solver for variable-density fluids is used. The interface is captured using a split Volume-of-Fluid method, generalized for a non-divergence-free liquid velocity and mass exchange across the interface. The importance of transcritical mixing effects over time for increasing pressures is shown. Initially, local deformation features differ considerably from previous incompressible works. Then, the minimal surface-tension force is responsible for the generation of overlapping liquid layers in favor of the classical atomization into droplets. Thus, surface-area growth at transcritical conditions is mainly a consequence of gas-like deformations under shear rather than spray formation.