The ability of matrix-assisted pulsed laser evaporation (MAPLE) technique to transfer and deposit high-quality thin organic, bioorganic, and composite films with minimum chemical modification of the target material has been utilized in numerous applications. One of the outstanding problems in MAPLE film deposition, however, is the presence of residual solvent (matrix) codeposited with the polymer material and adversely affecting the quality of the deposited films. In this work, we investigate the possibility of alleviating this problem by reducing the amount of matrix in the target. A series of coarse-grained molecular dynamics simulations are performed for a model lysozyme-water system, where the water serves the role of volatile "matrix" that drives the ejection of the biomolecules. The simulations reveal a remarkable ability of a small (5-10 wt %) amount of matrix to cause the ejection of intact bioorganic molecules. The results obtained for different laser fluences and water concentrations are used to establish a "processing map" of the regimes of molecular ejection in matrix-assisted pulsed laser deposition. The computational predictions are supported by the experimental observation of the ejection of intact lysozyme molecules from pressed lysozyme targets containing small amounts of residual water. The results of this study suggest a new approach for deposition of thin films of bioorganic molecules with minimum chemical modification of the molecular structure and minimum involvement of solvent into the deposition process.