Background/Objectives: Omeprazole undergoes degradation in acidic conditions, which makes it unstable in low pHs found in the gastric environment. The vast majority of already marketed omeprazole formulations use enteric polymer coatings to protect the drug from exposure to acidic pH in the stomach, allowing for drug release in the small intestine where the pH is higher. This study aimed to explore the technical aspects of using stomach acid neutralizers as an alternative to polymeric coatings for omeprazole. Methods: After evaluating various neutralizers, magnesium oxide and sodium bicarbonate were chosen to be incorporated into capsules containing omeprazole, which then underwent in vitro dissolution testing to assess their ability to maintain optimal pH levels and ensure appropriate dissolution kinetics. Hygroscopicity and chemical stability of the selected formulation were tested to prove pharmaceutical quality of the product. An in vivo pharmacokinetic study was conducted to demonstrate the efficacy of the omeprazole–sodium bicarbonate formulation in providing faster absorption in humans. Results: Sodium bicarbonate was selected as the most suitable antacid for ensuring omeprazole stabilization. Its quantity was optimized to effectively neutralize stomach acid, facilitating the rapid release and absorption of omeprazole. In vitro studies demonstrated the ability of the formulation to neutralize gastric acid within five minutes. In vivo studies indicated that maximum concentrations of omeprazole were achieved within half an hour. The product met the requirements of pharmaceutical quality. Conclusions: An easily manufacturable, fast-absorbing oral formulation was developed as an alternative to enteric-coated omeprazole.