This site already has several questions about how airplanes fly. Some of the answers do give useful insights, but the only real explanation I've found involves using a computer to solve the Navier-Stokes equations with a no-slip boundary condition (ref 1). By "real explanation," I mean one that actually predicts the amount of lift, starting from basic physics.
References 1 and 2 both suggest that an intuitive explanation might not be possible without significant input from computer calculations, but their definition of "intuitive" might be more restrictive than mine. I don't mind an explanation that relies on some advanced math, and I don't even mind if it only gives a very rough estimate, as long as it isn't computer-assisted.
To be more specific, consider the Kutta-Joukowski theorem, which already has a simple intuitive explanation. The K-J theorem relates the lift to the net circulation around the wing (under certain simplifying conditions), so if we had a non-computer-assisted way to estimate the net circulation, then we could put these pieces together to get a decent explanation of how airplanes fly.
Question: Can we estimate the circulation around an approximately flat thin airfoil$^\dagger$ under typical steady-state flying conditions, without any help from computers, using the no-slip condition and the basic principles that are used to deduce the Navier-Stokes equations?
Assuming the Kutta condition (that the flow leaves the surface only at the trailing edge) is fine. An argument that appeals to the starting-vortex might be okay (page 345 in ref 2), as long as it leads to a quantitative estimate valid for steady-state flying conditions.
$^\dagger$ I'm focusing on an approximately flat thin airfoil because this seems like the simplest case. Other conditions (like allowing a slightly rounded leading edge) are also welcome if they help simplify the argument.
McLean (2014), Understanding Aerodynamics: Arguing from the Real Physics, Wiley (https://onlinelibrary.wiley.com/doi/book/10.1002/9781118454190)
Anderson (2017), Fundamentals of Aerodynamics (sixth edition), McGraw Hill (https://www.mheducation.com/highered/product/fundamentals-aerodynamics-anderson/M9781259129919.html)
Here's a possibly related Big List question, but without any obvious matches in the list: