  This is the first part of a two paper sequence in which we prove the
global-in-x stability of the classical Prandtl boundary layer for the 2D,
stationary Navier-Stokes equations. In this part, we provide a construction of
an approximate Navier-Stokes solution, obtained by a classical Euler- Prandtl
asymptotic expansion. We develop here sharp decay estimates on these
quantities. Of independent interest, we establish \textit{without} using the
classical von-Mise change of coordinates, proofs of global in x regularity of
the Prandtl system. The results of this paper are used in the second part of
this sequence, [IM20] (arXiv:2008.12347), to prove the asymptotic stability of
the boundary layer as $\eps \rightarrow 0$ and $x \rightarrow \infty$.
