You need to create an account to access download links (and I only see this option for songs I've generated). However, it looks like each link simply points to an mp3 file based on the song id. eg:
1. Open the website https://app.suno.ai/.
2. Click on the share button above any song to obtain the share URL.
3. Paste the URL onto our website https://sunoaidownload.com/.
4. Click 'Download'.