You can use the \AddToShipoutPictureBG command from the eso-pic package together with a \put(0,0){ ...} to place your tikzpicture in the upper left corner of the page. Usually, for positioning TikZ objects relative to the page, one would use \tikz[remember picture, overlay] together with the (current page) node, but that requires two compile runs. This approach only needs one.
If you then set x=\paperwidth, y=-\paperheight, the coordinate (1,1) will be the lower right corner.
You can then position objects within your tikzpicture as usual:
\node at (0,1) [anchor=south west, scale=4] {Lower Left};
\node at (1,1) [anchor=south east, scale=4] {Lower Right};
\node at (0,0) [anchor=north west, scale=4] {Upper Left};
\node at (1,0) [anchor=north east, scale=4] {Upper Right};
% \fill [ultra thick, orange] (0.5,0.5) circle [radius=2cm];
\draw (0,0) -- (1,1);
will produce

\documentclass{article}
\usepackage{tikz}
\usepackage{longtable}
\usepackage{afterpage}
\usepackage{lipsum}
\usepackage[texcoord]{eso-pic}
\begin{document}\lipsum[3]
\AddToShipoutPictureBG*{%
\put(0,0){%
\tikz [
overlay,
x=\paperwidth,
y=-\paperheight] {
\node at (0,1) [anchor=south west, scale=4] {Lower Left};
\node at (1,1) [anchor=south east, scale=4] {Lower Right};
\node at (0,0) [anchor=north west, scale=4] {Upper Left};
\node at (1,0) [anchor=north east, scale=4] {Upper Right};
%
\fill [ultra thick, orange] (0.5,0.5) circle [radius=2cm];
\draw (0,0) -- (1,1);
}
}
}
\end{document}