This paper presents a model-agnostic analysis of the universe's expansion history using Gaussian process (GP) regression, combining Pantheon-Plus supernova Ia (SN-Ia) data with Baryon Acoustic Oscillation (BAO) measurements from SDSS-IV and DESI DR1. The ΛCDM model is consistently included within the 95% confidence intervals in both reconstructions. The study finds evidence that the DESI Luminous Red Galaxy (LRG) data at \( z_d = 0.51 \) is not an outlier. The analysis of \( \Omega_m \) diagnostics and the total equation of state (EoS) suggests a quintessence-like dark energy scenario with a slowly varying EoS and a phantom-crossing at higher redshifts. When considering additional SN-Ia compilations (DES-5YR and Union3) in combination with DESI BAO, the ΛCDM model is excluded outside the 3σ confidence levels for DESI + DES-5YR, while it remains within 1σ for DESI + Union3. The results indicate a \(\approx 2\sigma\) discrepancy between the DESI + Pantheon-Plus and DESI + DES-5YR data sets, highlighting the need for further investigation. The study also explores the consistency between different data sets and the implications of the DESI BAO data on the Hubble constant \( H_0 r_d \).This paper presents a model-agnostic analysis of the universe's expansion history using Gaussian process (GP) regression, combining Pantheon-Plus supernova Ia (SN-Ia) data with Baryon Acoustic Oscillation (BAO) measurements from SDSS-IV and DESI DR1. The ΛCDM model is consistently included within the 95% confidence intervals in both reconstructions. The study finds evidence that the DESI Luminous Red Galaxy (LRG) data at \( z_d = 0.51 \) is not an outlier. The analysis of \( \Omega_m \) diagnostics and the total equation of state (EoS) suggests a quintessence-like dark energy scenario with a slowly varying EoS and a phantom-crossing at higher redshifts. When considering additional SN-Ia compilations (DES-5YR and Union3) in combination with DESI BAO, the ΛCDM model is excluded outside the 3σ confidence levels for DESI + DES-5YR, while it remains within 1σ for DESI + Union3. The results indicate a \(\approx 2\sigma\) discrepancy between the DESI + Pantheon-Plus and DESI + DES-5YR data sets, highlighting the need for further investigation. The study also explores the consistency between different data sets and the implications of the DESI BAO data on the Hubble constant \( H_0 r_d \).