The growing demand for global wind power production, driven by the critical need for sustainable energy sources, requires reliable estimation of wind speed vertical profiles for accurate wind power prediction and comprehensive wind turbine performance assessment. Traditional methods relying on empirical equations or similarity theory face challenges due to their restricted applicability beyond the surface layer. Although recent studies have utilized various machine learning techniques to vertically extrapolate wind speeds, they often focus on single levels and lack a holistic approach to predicting entire wind profiles. As an alternative, this study introduces a proof-of-concept methodology utilizing TabNet, an attention-based sequential deep learning model, to estimate wind speed vertical profiles from coarse-resolution meteorological features extracted from a reanalysis dataset. To ensure that the methodology is applicable across diverse datasets, Chebyshev polynomial approximation is employed to model the wind profiles. Trained on the meteorological features as inputs and the Chebyshev coefficients as targets, the TabNet more-or-less accurately predicts unseen wind profiles for different wind conditions, such as high shear, low shear/well-mixed, low-level jet, and high wind. Additionally, this methodology quantifies the correlation of wind profiles with prevailing atmospheric conditions through a systematic feature importance assessment.