Was just thinking about this - the thing is, even if Ancyra never runs out of supplies or fuel, the player will eventually run out of credits.
Though one thing that should be noted: there's a bug where, if you arrive to Ancyra with the recovered ships and they're mothballed, they don't count for the supplies you get, and they don't get repaired, so that's a massive supply sink. This is fixed for the next release - mothballed ships will get automatically unmothballed and fully repaired on this tutorial step. I suspect that this might be the likely cause of the issue, and/or recovering too many ships.
When starting with one of the faster starts, I'd suggest only recovering 2-3 of the better ships - you only really need more when using the start options that give you a pair of frigates, and more ships = more supplies used. If you basically follow the tutorial instructions and don't get too sidetracked, you should have enough supplies.
(On a side note, "make sure your supply situation can handle your activities" is a valid lesson that applies elsewhere in the game. Yeah, it's a sandbox, but supply-based time pressure is part of the game, you know? But that doesn't necessarily means that the tutorial is tuned right with regards to this, and, right, there's also the aforementioned bug.)
Hi, and welcome to the forum, by the way!