You can listen to a downloaded subliminal without an internet connection when the audio file is stored locally and your player can open it. A link in an order email or a file listed in cloud storage doesn't by itself confirm that the audio is available offline.
Save the actual audio
Complete the download and extract the ZIP if your order uses one. Keep the MP3 in a folder you can find, then open or import it into your chosen player. Follow the iPhone or Android instructions for those devices.
If your file manager shows that the file is stored in the cloud, use its option to download or keep the file on the device. The name of that option depends on the app.
Test the conditions you'll use
Disconnect from the internet and open the track again. Try a section later in the file as well as the beginning. This checks whether the whole recording is available.
For repeat playback, enable your player's repeat setting and check what happens at the end. Lock the screen if you intend to listen that way. Playback in the background and repeat behaviour depend on the player.
Keep your own copy
A backup of your downloaded files saves you from relying on an old email or a future download. Keep the program name with the audio so you know which recording you're opening.
For a Studio export, download the finished WAV or MP3 and run the same offline check. Studio's saved projects and in-app listening features have their own storage rules; the exported file is what this check covers.