Global trends in health, climate, and population growth drive the demand for high-nutrient plants like spinach, which thrive under controlled conditions with minimal resources. Despite technological advances in agriculture, current systems often rely on traditional methods and need robust computational models for precise plant growth forecasting. Optimizing vegetable growth using advanced agricultural and computational techniques, addressing challenges in food security, and obtaining efficient resource utilization within urban agriculture systems are open problems for humanity. Considering the above, this paper presents an enclosed agriculture system for growth and modeling spinach of the Viroflay (Spinacia oleracea L.) species. It encompasses a methodology combining data science, machine learning, and mathematical modeling. The growth system was built using LED lighting, automated irrigation, temperature control with fans, and sensors to monitor environmental variables. Data were collected over 60 days, recording temperature, humidity, substrate moisture, and light spectra information. The experimental results demonstrate the effectiveness of polynomial regression models in predicting spinach growth patterns. The best-fitting polynomial models for leaf length achieved a minimum Mean Squared Error (MSE) of 0.158, while the highest MSE observed was 1.2153, highlighting variability across different leaf pairs. Leaf width models exhibited improved predictability, with MSE values ranging from 0.0741 to 0.822. Similarly, leaf stem length models showed high accuracy, with the lowest MSE recorded at 0.0312 and the highest at 0.3907.