Error on install page

After uploading, renaming config files and setting permissions, I can't open the install page. The following error appears:

Warning: require(XXX/system/storage/vendor/composer/../react/promise/src/functions_include.php): failed to open stream: No such file or directory in /XXX/system/storage/vendor/composer/autoload_real.php on line 66
Fatal error: require(): Failed opening required 'XXX/system/storage/vendor/composer/../react/promise/src/functions_include.php' (include_path='.') in /XXX/system/storage/vendor/composer/autoload_real.php on line 66

How can I get OpenCart 3.0.2.0 working on my shared hosting? PHP version is 7.3.

Ensure to upload your ZIP file from your host File Manager console. Then, use the 'Extract' button to deflat the files rather than uploading files via FTP which can cause missing files to be uploaded during the process.

My host doesn't provide a file manager. I uploaded all files several times to ensure there weren't any files missing. But I don't think the error is because of a missing or corrupt file, looks like a problem with composer?

Sorry reading that you have troubles.
But as it seems, you have not used the correct package.

1. Download from here (3.0.3.1) https://www.opencart.com/index.php?route=cms/download
2. Unzip locally and transfer files from folder upload with a FTP-Client (e.g. Filezilla) to your server.
3. Then rename the 2 config-dist.php to config.php
4. Call the installer in you webbrowser