The phase landscape of UTe$_2$ features a remarkable diversity of superconducting phases under applied pressure and magnetic field. Recent quantum oscillation studies at ambient pressure have revealed the quasi-2D Fermi surface of this material. However, the pressure-dependence of the Fermi surface remains an open question. Here we track the evolution of the UTe$_2$ Fermi surface as a function of pressure up to 19.5 kbar by measuring quantum interference oscillations. We find that in sufficient magnetic field to suppress both superconductivity at low pressures and incommensurate antiferromagnetism at higher pressures, the quasi-2D Fermi surface found at ambient pressure smoothly connects to that at 19.5 kbar, with no signs of a reconstruction over this pressure interval. The warping of the cylindrical Fermi sheets continuously increases with pressure, which is consistent with increased $f$-orbital contribution at the Fermi level, up to and beyond the critical pressure at which superconductivity is truncated. These findings highlight the value of high pressure quantum interference measurements as a new probe of the electronic structure in heavy fermion materials.
