If you do not wish to use Jetpack or a lighter version of it that provides this feature or Gary Jones' plugin that relies on Jetpack, the 'original' Infinite Scroll script's WordPress version can be used.
Let's see how Infinite-Scroll plugin can be used to automatically (or on click) load the next set of Posts right below the existing ones on Posts page and other listing pages like archives and search results in your Genesis site.
Install and activate Infinite-Scroll plugin.
Go to Settings > Infinite Scroll and change the selectors like so:
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