I have array of mobile numbers, around 50,000. I\'m trying to process and send bulk SMS to these numbers using third-party API, but the browser will freeze for some minutes
Cronjob would be your best bet, I don't see why it would take any longer than doing it in the browser if your only problem at the moment is the browser timing out.
If you insist on doing it via the browser then the other solution would be doing it in batches of say 1000 and redirecting to the same script but with some reference to where it got up to last time in a $_GET variable.