Human leukocyte antigen (HLA) compatibility is critical for the success of hematopoietic stem cell transplantation, particularly for patients without matched related donors. As cord blood units (CBUs) play a growing role in bridging donor gaps, cord blood banks must optimize donor selection and CBUs’ storage to maximize HLA diversity. A prenatal, pre-collection prediction framework is developed to estimate whether a CBU’s future HLA profile will be rare or common within a large banking registry. Rarity was defined as a binary label based on observed 6/6 low-resolution matches at the HLA-A, HLA-B, and HLA-DRB1 loci (0 matches = rare; ≥1 = common). Demographic, medical, and obstetric features were preprocessed via one-hot encoding, degree-2 polynomial expansion, and Principal Component Analysis (PCA); feature selection used Random Forest (RF) importance within a leakage-controlled pipeline. Five machine learning models, including K-Nearest Neighbors (KNN), RF, XGBoost, and a deep multilayer perceptron (MLP), are used, with each evaluated with and without Genetic Algorithm (GA) hyperparameter tuning on identical cross-validation folds, and a TOPSIS multi-criteria ranking was performed to rank algorithms. The GA-tuned MLP performs best (Accuracy 0.74, ROC-AUC 0.84) and ranks first by Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), with GA-tuned XGBoost close behind. These results demonstrate that prenatal, pre-collection prediction of HLA rarity is feasible and can support prioritization for confirmatory genotyping to enhance diversity in cord-blood inventories.