How Telegram phone verification works
Telegram's verification confuses people because the code does not always arrive by SMS — and that is by design rather than a fault.
In-app first, SMS second
If the number is already signed in on another device, Telegram delivers the code to that session inside the app and never sends an SMS. On a brand-new number there is no session to deliver to, so the code goes by SMS as expected.
The number is the login
Like WhatsApp, Telegram identifies accounts by phone number. Usernames are display handles, not credentials — losing the number means losing the route back in, unless you have set a two-step password and can still receive the code.
If nothing arrives
Wait the full timer before re-requesting; repeated requests can rate-limit the number. If it still fails, a different country is usually more productive than another attempt on the same one.