How do I generate a 20,000 x 20,000px png?

It is possible but none of our free services will do that for you. You have to understand that producing such large images does require a lot of resources - and while we give away OSM data for free, the amount of computing power that we can give away is limited.

There are several ways for you to acquire such an image. For example, you could download an SVG or PDF image from the export tab and then use a program like rsvg to produce a bitmap from the SVG. Or, you could render an image yourself using either your own Mapnik installation (powerful but a lot of work to set up - use that if you are on Linux and expect to render images like that more often) or a standalone renderer like Maperitive (runs on Linux and Windows). Details on both techniques can be found on our wiki.

There's also the option of using a third-party service. The free Maposmatic generates large PNGs (albeit not the 400 Megapixel you're after) and PDFs. Some of the businesses listed on the Commercial OSM Software and Services page will also be able to produce such images as a paid service.

some more hints:

how-do-i-export-map-images-of-larger-areas

create-a-wall-map-of-an-area-50-kilometers-by-120-kilometers

Check out Viking GPS. While designed to work with GPS data, it also has the ability to output any map it is displaying to a graphic file (or files) in whatever resolution you choose. The data can come from any supported source, including several different OSM data tile source (Mapnik, osmarender, maplint). It is also possible to setup your own sources (TOPOsm, Yahoo, Google, Cloudmade styles). [It shouldn't need to be said, but be sure to check the licensing of the sources.]

BTW, If you do use Viking with any of the OSM tile sources, then please ensure you are following the Tile Usage Policy by setting your tile checking period to 7 days (Viking->Edit->Preferences->Tile Age = 604800). In versions prior to 1.2.2, it was inadvertently set to small (30 seconds).

You could also use ffmpeg or imagemagik to combine multiple smaller images into a single image.

Try this: https://www.imagemagick.org/discourse-server/viewtopic.php?t=11672