Is there a way to by-pass the pagination function on one custom template?

The best way to do this is to use the pre_get_posts filter, which changes the main query. That way you’re not running the default query plus a custom one on top of it. You’ll have to determine the “if” conditions to only run on the query you want to affect:

<?php
function wpse_366882_get_all_posts($query) {
    // This will run for all main queries that are not in wp-admin.
    // You may want "is_archive()", "is_page('slug')" or some other condition.
    if ( ! is_admin() && $query->is_main_query() ) {
    // Setting to -1 shows all.
        $query->set( 'posts_per_page', -1 );
    }
}
add_action( 'pre_get_posts', 'wpse_366882_get_all_posts' );
?>

You can place this code in a custom plugin, or in a custom theme or child theme’s functions.php file.