There is currently no way to download the full audit log.

You are limited to 50k records per search/download, we have hundreds of gb of data to download, and searching further limits our results. It would take years to download all the data this way, and therefore is not usable. 3rd Party solutions will take weeks/months to download this amount of data also, and also require using filtering to get data, which limits the results to less than a full download.