The DESI 2024 BAO data suggest a dynamical dark energy (DE) scenario when combined with CMB and SNIa data, indicating a crossing of the phantom divide. This result challenges standard quintessence models, which cannot cross the divide without instabilities. A non-parametric reconstruction of the DE equation of state confirms the need for a phantom crossing. The study explores Horndeski gravity models and identifies non-minimal coupling as the key modification enabling a stable phantom crossing. The Thawing Gravity model, a non-minimally coupled Horndeski theory, matches DESI observations and provides a better fit than ΛCDM for BAO, CMB, and SNIa data. It naturally incorporates non-minimal coupling and offers a viable framework for both early and late DE/MG scenarios. The model's parameters are similar to the w0wa CDM model, and it shows improved fits with Δχ² values of -2.1, -1.8, and -1.9 for DESI, CMB, and SNIa, respectively. The model's dynamics, with a scalar field initially frozen and thawing at low redshift, align with DESI data. The study highlights the importance of non-minimal coupling in stabilizing phantom crossing and supports the theoretical viability of the Thawing Gravity model. The results emphasize the need for further investigation into the unification of early and late DE/MG scenarios.The DESI 2024 BAO data suggest a dynamical dark energy (DE) scenario when combined with CMB and SNIa data, indicating a crossing of the phantom divide. This result challenges standard quintessence models, which cannot cross the divide without instabilities. A non-parametric reconstruction of the DE equation of state confirms the need for a phantom crossing. The study explores Horndeski gravity models and identifies non-minimal coupling as the key modification enabling a stable phantom crossing. The Thawing Gravity model, a non-minimally coupled Horndeski theory, matches DESI observations and provides a better fit than ΛCDM for BAO, CMB, and SNIa data. It naturally incorporates non-minimal coupling and offers a viable framework for both early and late DE/MG scenarios. The model's parameters are similar to the w0wa CDM model, and it shows improved fits with Δχ² values of -2.1, -1.8, and -1.9 for DESI, CMB, and SNIa, respectively. The model's dynamics, with a scalar field initially frozen and thawing at low redshift, align with DESI data. The study highlights the importance of non-minimal coupling in stabilizing phantom crossing and supports the theoretical viability of the Thawing Gravity model. The results emphasize the need for further investigation into the unification of early and late DE/MG scenarios.