We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extensive treatments of QCD. Furthermore, we obtain a non-trivial x-dependence of the «(p⊥)2 » and some consistency with the Gaussian ansatz but only in the small (p⊥)2 region. Those features suggest our results may be a useful alternative in future experimental extractions.