Padding to CSS Grid

You can add padding between the grid containers using grid padding or row gap, depending on your needs.

gap

row-gap

column-gap

Otherwise I would need a more detailed question to solve your issue.

It's difficult to understand what you want to accomplish based on your post, but it looks like the padding does not take place because your CSS rule is not properly targeting the element. Moving the padding into the header rule, as seen below, does apply the padding.

header{
    width:100%;
    height: 5%;
    color: #fff;
    background: #434343;
    display: grid;
    grid-template-columns: 2fr auto;
    padding:500px;
}


header:not(menu, h1, nav){
    display: block;
    /*padding:500px;*/

}

<header>
test
</header>