Is it possible to create a post page and put the recent posts on the homepage?

@valeska: For this, you’ll need to create a child theme. You can find more details on creating child theme HERE. Then in your child theme, create a new-file for page template, and add the following code:

<?php
/**
 * Template Name: My page
 *
 */

get_header(); ?>

	<main id="main" class="site-main" role="main">

		<?php while ( have_posts() ) : the_post(); ?>

			<?php get_template_part( 'content', 'page' ); ?>

			<?php 
				/** 
				 * fullframe_comment_section hook
				 *
				 * @hooked fullframe_get_comment_section - 10
				 */
				do_action( 'fullframe_comment_section' ); 
			?>

		<?php endwhile; // end of the loop. ?>

		<?php // Display blog posts on any page
		$temp = $wp_query; $wp_query= null;
		$wp_query = new WP_Query(); $wp_query->query('&paged='.$paged);
		while ($wp_query->have_posts()) : $wp_query->the_post(); ?>

		<?php
			/* Include the Post-Format-specific template for the content.
			 * If you want to override this in a child theme then include a file
			 * called content-___.php (where ___ is the Post Format name) and that will be used instead.
			 */
			get_template_part( 'content', get_post_format() );
		?>

		<?php endwhile; ?>

		<?php if ($paged > 1) { ?>

		<nav id="nav-below" role="navigation">
        	<h3 class="screen-reader-text">Post navigation</h3>
        	<div class="nav-previous"><?php next_posts_link('&larr; Older Posts'); ?></div>
        	<div class="nav-next"><?php previous_posts_link('Newer Posts &rarr;'); ?></div>
        </nav>

		<?php } else { ?>

		<nav id="nav-below" role="navigation">
        	<h3 class="screen-reader-text">Post navigation</h3>
        	<div class="nav-previous"><?php next_posts_link('&larr; Older Posts'); ?></div>
        </nav>

		<?php } ?>

		<?php wp_reset_postdata(); ?>

	</main><!-- #main -->

<?php get_sidebar(); ?>
<?php get_footer(); ?>

Then add a new page and select this custom template, then it will display the page content along with the recent posts.

Note: Please make sure you have selected the very page as the static front page.

Regards,
Mahesh