I’ve tried running Telegram ads a couple of times, and the delivery time wasn’t always consistent. Sometimes they started showing within the first hour, and other times I had to wait several hours before seeing any impressions. It seemed like the review stage and how specific the targeting was played a big role in the delay.
If everything is set up correctly and the audience size isn’t too narrow, they should begin delivering without much trouble. I wouldn’t stress if there’s a delay at first, though—just keep an eye on the dashboard to make sure nothing gets stuck in review or rejected.