If you use BuddyPress as the 'Registration Page URL' within Event Espresso -> Reg Form -> User Integration Settings this allows you to automatically log the user in when they create an account and redirect them back to the checkout to continue the registration.

example.php

<?php //Please do not include the opening PHP tag if you already have one

//Function to allow you to use BuddyPress registration as for site registrations during the EE Checkout
//and then redirect them back to the checkout.
function tw_ee_bp_redirect($user_id) {
    $checkout = EE_Registry::instance()->SSN->checkout();

    if( $checkout instanceof EE_Checkout ) {
        
        $user = get_user_by( 'id', $user_id);
        if( $user ) {
            wp_set_current_user( $user->ID, $user->user_login );
            wp_set_auth_cookie( $user->ID );
            do_action( 'wp_login', $user->user_login );

            wp_safe_redirect( $checkout->reg_page_base_url );
            exit;
        }
    }
}
add_action('bp_core_signup_user', 'tw_ee_bp_redirect', 100, 1);