... How much drugs are we talking here?
I don't know. It depends on a few variables. You jump to level 2 after finishing the first battle. If you spend story points on things to get bonus XP (hire and mentor officers, etc) you can rack a lot of bonus XP, and then fighting the 5 pirate fleets can bring you to level 3.5-just about 4. A few months of smuggling can earn you the XP to get over lvl 5 and maybe even to lvl 6. There are also 3 salvage fields that can earn you a bit of XP, in addition to the 8 derelicts (you can recover/salvage them and mothball them before the probe fight). If you're going with a classic (2 frigate) start, the easiest way to smuggle enough quickly would be to take the wayfarer+shepherd combo. You can also sometimes find heavily d-modded shepherds and wayfarers for sale at either station.
Drugs (Ancyra) <-> Organs (Derinkuyu) is always a guaranteed profit, yielding good XP per units trafficked.
Food (Ancyra) <-> Luxury Good, Domestic Goods, Organics, Supplies, Fuel (Derinkuyu) can be slightly profitable to fill the extra space, but if you overdo it the profit can vanish and you have to wait a bit for it to become profitable again.
You can also take advantage of cheap supplies and fuel on Ancyra and sell it to Derinkuyu before they remember they're cut off and jack the prices up. Recovering the ships at Tetra (specifically the Dram) before heading over to Ancrya and clearing Ancyra out of fuel (both open market and black market) to sell off at Derinkuyu can yield profit of $30+ per unit. These both can provide massive initial XP gains.
Overall it can be a great kickstart. 4+ months of smuggling and you can walk away with about 1 million credits. And if you're doing a salvage/"buy nothing" play-through, getting the AI skill and those 2-3 extra explorarium frigates at the start can really help; they can deploy for 1 supply each, if they blow up you only lose ~3 supply and no crew each, they're guaranteed recoverable even without reinforced bulkheads (unless you're over the ship max), and if you're super lucky with your seed you can get an extra gamma core from the probe to use as a lvl 3 officer for one of them. Sentries are decent missile harassers (swarmers / salamanders) to avoid your fleet being swarmed or as suicide bombers (hammerheads) to kill off cruisers, and wardens can bring a decent punch with a chain gun + machine gun combo, given they both only cost 1 supply to field. You'll retire them eventually, but early game they can help out.
Just don't overdo it. It may have been patched up, but in .95 if you went more than about a year without stabilizing the jump points, Derinkuyu would de-civilize. And if you hadn't already at least contacted the agent, you'd be locked from being able to complete the tutorial (de-civilized = no comm directory at the station = can't speak to the agent to get the algorithm).