Since everyone has a shadow self, the question of 'why did Souji's shadow not appear?' comes to mind. Well, to go farther back on this, lets look on the shadows we know and why they appeared.

Shadows are the fears, anxieties and negative emotiones of one's self. All shadows since Yukiko had a dungeon and made the inner conflict of their selfs pretty clear. The only two who were a bit different were Yosuke and Chie, who had no dungeon, but a clear conflict.

My guess is, depending on how long those negative feelings are bottled up inside one's self, it creates a dungeon in the TV world. Therefore Yosuke and Chie had not enough time to create a dungeon - Yosuke mourned Saki's death and wanted answers, so they went into the TV a few days after Saki was murdered (not enough time to create a dungeon). Chie probably had anxiety of losing Yukiko right after she saw her friend on the Midnight Channel ('If Yukiko gets a boyfriend, she doesn't need me anymore'). She joined the rescue group right after Yukiko appeared on TV and encountered her Shadow (and again: not enough time to come up with a dungeon).

Jumping to Souji again. He didn't encounter his shadow in order to get his Persona. Why was there no shadow?

Souji came to Inaba, into an unknown family, where he had noone to relate to. He might worry a bit about his parents and friends he left behind, but he probably worried more about what was ahead of him: 'Will I get along with Dojima and Nanako? Will I make friends at school?'

I don't think these worries were strong enough to awaken his shadow yet. He got along with Dojima and Nanako somehow and even made a friend the first week. Then he got a Persona (like 'Wow, a fantasy world where I have special powers??? This is so cool, no time for depressing thoughts') and well, no potential for his shadow to appear.

There are many fics out there who tackled the possibility of a shadow version of Souji, and they nailed it down quite nicely. What would be Souji's fear?

Since the protagonist is voiceless and has no real character, there's room to imagine. The player (who controls Souji) wants to make him perfect stat-wise and Social Link-wise. So maybe Souji is something like a popular guy.

And here it comes down: When you're popular and have a huge group of friends, PLUS being a leader of a group, you might fail your friends. You might dissappoint them, because you have to turn them down when they wanna hang out. You might reject their confessions, when you've reached a certain point in the relationship (the typical 'friend or lovers'-choice you get when you date the girls). You might make the wrong decisions which lead your party into a death trap and get all of them killed. So yeah, it really is a lot of pressure.

So many 'what if'-scenarios may even cause continuous anxiety and then there are your groups expectation's, too, you don't want to let them down, and seriously, how the hell do you even handle it.

Over time, Souji boosts his stats with different activities. But this doesn't mean he's confident or anything. There's always the fear of failing. (You can pursue it even further: Maybe Souji isn't confident enough to reject a girl's confession the first time - 'I don't wanna hurt her' and 'She's been nice to me', so he will agree to date her, but he just wanted to be friends. And maybe it doesn't happen once, but a few times, where he said yes to something he didn't want.)

I guess it'll come gradually with no real trigger (you know, as I said: bottling up your negative emotions), it just piles up/accumulates and then, suddenly, it snaps. (This is basically the main idea in fanfics.)

With the more Social Links and progress of story, I'd say it's more plausible that Souji's shadow comes to light. He even might have a dungeon.

I think of something similar to Yukiko/Kanji's dungeon, a setting where the partymembers are in an actual dating show. Shadow!Souji is all charming and explains the rules; that he'll give items to the people who might progress further, because he likes them, and the others have to leave. Which leaves the unchosen ones stuck, because they can't go any further. The party members become fewer in number, but they go on. The higher they advance, the more Shadow!Souji is irritated why they are even here, because he never wanted anyone to come, they pressure him and he wants them to go. In the end, only Kanji and Yosuke make it to the last floor, because 'you guys were my friends, you didn't pressure me to do things I didn't want and talked me into it, even when you guys relied so much on me that I could easily lead you to your death and you'd happily follow my lead; why are you not going to be responsible for yourselves and leave the alone, I never wanted to be a leader in the first place, stop pressuring me!'