How to Load Posts on Demand in Genesis. https://sridharkatakam.com/load-posts-demand-using-ajax-genesis/

functions.php

/**
 * AJAX Load More
 * @link http://www.billerickson.net/infinite-scroll-in-wordpress
 */
function be_ajax_load_more() {

	$args = isset( $_POST['query'] ) ? array_map( 'esc_attr', $_POST['query'] ) : array();
	$args['post_type'] = isset( $args['post_type'] ) ? esc_attr( $args['post_type'] ) : 'post';
	$args['paged'] = esc_attr( $_POST['page'] );
	$args['post_status'] = 'publish';

	ob_start();
	$loop = new WP_Query( $args );
	if( $loop->have_posts() ): while( $loop->have_posts() ): $loop->the_post();
		printf( '<article %s>', genesis_attr( 'entry' ) );

			do_action( 'genesis_entry_header' );

			do_action( 'genesis_before_entry_content' );

			printf( '<div %s>', genesis_attr( 'entry-content' ) );
			do_action( 'genesis_entry_content' );
			echo '</div>';

			do_action( 'genesis_after_entry_content' );

			do_action( 'genesis_entry_footer' );

		echo '</article>';
	// endwhile; endif; wp_reset_postdata();
	endwhile; if ( $_POST['page'] < $loop->max_num_pages ) { echo '<button class="load-more">Load More</button>'; } endif; wp_reset_postdata();
	$data = ob_get_clean();
	wp_send_json_success( $data );
	wp_die();
}
add_action( 'wp_ajax_be_ajax_load_more', 'be_ajax_load_more' );
add_action( 'wp_ajax_nopriv_be_ajax_load_more', 'be_ajax_load_more' );

/**
 * Template Redirect
 * Use template_load-more.php for Posts page and all archives.
 */
add_filter( 'template_include', 'custom_blog_archives_template', 99 );
function custom_blog_archives_template( $template ) {

	if ( is_home() || is_archive() ) {
		$new_template = locate_template( array( 'template_load-more.php' ) );
		if ( '' != $new_template ) {
			return $new_template ;
		}
	}

	return $template;
}

load-more.js

jQuery(function($){

	// $('.post-listing').append( '<button class="load-more">Load More</button>' );
	// var button = $('.post-listing .load-more');
	var page = 2;
	var loading = false;

	$('body').on('click', '.load-more', function(){
		if( ! loading ) {
			loading = true;
			$(this).remove();
			var data = {
				action: 'be_ajax_load_more',
				page: page,
				query: beloadmore.query,
			};
			$.post(beloadmore.url, data, function(res) {
				if( res.success) {
					$('.post-listing').append( res.data );
					// $('.post-listing').hide().append( res.data ).fadeIn(500); // to have fadeIn effect
					// $('.post-listing').append( button );
					page = page + 1;
					loading = false;
				} else {
					// console.log(res);
				}
			}).fail(function(xhr, textStatus, e) {
				// console.log(xhr.responseText);
			});
		}
	});

});

style.css

.post-listing {
	margin-bottom: 40px;
}

.load-more {
	display: table;
	margin: 0 auto;
}

template_load-more.php

<?php

/**
 * Javascript for Load More
 *
 */
function be_load_more_js() {

	global $wp_query;
	$args = array(
		'url'   => admin_url( 'admin-ajax.php' ),
		'query' => $wp_query->query
	);

	wp_enqueue_script( 'be-load-more', get_stylesheet_directory_uri() . '/js/load-more.js', array( 'jquery' ), '1.0', true );
	wp_localize_script( 'be-load-more', 'beloadmore', $args );

}
add_action( 'wp_enqueue_scripts', 'be_load_more_js' );

add_action( 'genesis_before_loop', 'sk_opening', 20 ); // a high priority of 20 to make this appear below .archive-description
function sk_opening() {
	echo '<div class="post-listing">';
}

add_action( 'genesis_after_loop', 'sk_closing' );
function sk_closing() {
	// echo '</div>';
	echo '<button class="load-more">Load More</button></div>';
}

// Remove Archive Pagination
remove_action( 'genesis_after_endwhile', 'genesis_posts_nav' );

genesis();

Great code! Thank you for sharing.