Dear Will, have you ever heard about figure of speech?  that´s an expression used in a different way, to give us a picture in our minds.

    In this light,  "doing something under the sun" is used in the sense of which activities are more usual to a group or to somebody in special, that is, the most likely or mundane thing to somebody.    The everyday activity we fancy.

    I think you got it already, see it?

    Nothing to do with people beaching all day, and tanning in the process!

    Some examples of what I just explained, taken from the Bible:

    ECLESIASTES 01:
3 Que proveito tem o homem, de todo o seu trabalho, que faz debaixo do sol?
3 What does man gain by all the toil at which he toils under the sun?

5 Nasce o sol, e o sol se põe, e apressa-se e volta ao seu lugar de onde nasceu.

5 The sun rises and the sun goes down, and hastens to the place where it rises.

9 O que foi, isso é o que há de ser; e o que se fez, isso se fará; de modo que nada há de novo debaixo do sol.
9 What has been is what will be, and what has been done is what will be done; and there is nothing new under the sun.

ECLESIASTES 02:
19 E quem sabe se será sábio ou tolo? Todavia, se assenhoreará de todo o meu trabalho que realizei e em que me houve sabiamente debaixo do sol; também isto é vaidade.
19 and who knows whether he will be a wise man or a fool? Yet he will be master of all for which I toiled and used my wisdom under the sun. This also is vanity.

  PP.