If it was still the ~500m days of PLEX I'd say you could easily do it. However at the ~1bn price point now, I'm not too sure.
In theory PLEX prices should come down depending on how new player Alpha retention and Alpha to Omega conversion is.
I think the best way for an alpha to actually fund a PLEX subscription is via trading or ratting.
If you are returning and have a bit of money already for investing in the market, then you should be able to do it.
The skills available for trade is:
Broker relations II
Marketing II
Trade III
As you can see it's not great for low margin trading since you can't reduce broker fees and sales tax due to locked out and limited skills so there's things on the market you will trade at a loss with due to their margins being so low only full trading skills can turn a profit of like many high volume ships.
So you are limited to mostly low volume to be really effective and high priced (higher margin) items on Jita... there's quite a lot of them actually and great if you have a lot of money to invest since you can make up the low volume issue by basically investing in all the low volume items to have a decent cash flow... again this needs a lot of ISK to begin with.
However you do not need to trade in Jita, you can do so in Amarr for example, it has across the board higher margins and still fairly good volumes being moved.
I've never run missions to make ISK (hell, in over a decade playing, I've barely run missions at all), the only way I make ISK is via trading, and back when I lived in wormholes (was in Aperture Harmonics) from sleeper farming and such.
Otherwise I think ratting in lowsec and nullsec are the best ISK per hour for an alpha clone in a cruiser (you could use a navy faction one if you want but a normal tech 1 should suffice). Specifically you could try ratting for those rats that drop Security Tags in low sec, you should be able to handle them with an Alpha cruiser. Back when Security Tags were introduced I seriously made 500m ISK in 2 hours of ratting and it was super easy for me in a Tech 2 frigate (used a Harpy). Sure the various tags have come down in price since then but they're still not too bad, the Clone Soldier Negotiator Tag and Clone Soldier Transporter Tag fetch 15-20m. Plus you get the usual bounties on top of it as well and the tags are guaranteed to drop if the rat spawns.
If I remember correctly the rarity of the special rats that drop these tags are based on system security level, and I will post a great lowsec pocket that in the past made me farm them really quickly.
http://evemaps.dotlan.net/map/Placid/Barleguet
(areas within red selection)
As you can see it's also an easy access to Syndicate NPC 0.0. You can either sell them the tags at Jita or just sell them at the CONCORD stations in one of those low security systems since people who want to repair security status needs to visit one of those stations in particular to do so and can just buy it straight from there. Aulbres has two stations that many people tend to use.
No idea what Faction Warfare is like now for ISK.