Every 5e campaign I've run has started at 1st level.
For previous editions that's a little less true: of two 4e games I ran, one was at 1st level, the other at 10th. Neither made it to a second session. All (I think) of the 3e campaigns I ran started at 1st level, and there were a good many of them. (I did run a number of one-shots that varied in level.) Most of the 2nd Edition games I ran started at 3rd level following a recommendation in the "Complete Fighters Handbook". In hindsight, I no longer consider that to be good advice.
Overall, I think 5e has it right: I much prefer starting at 1st level, but I want those first couple of levels to go quickly.