Having only 1 character is 4x harder than if you have 2 characters. Because you not only have twice the firepower with 2 characters, but you also have twice the HP.
As an example, consider a character with 10 HP, dealing 1 dmg per attack, fighting a monster with the same stats. It's a 50/50 battle, with someone barely surviving with 1 HP and the other dead during the 10th round. But have 2 of those characters fight 1 monster, and the characters will kill the monster in 5 turns. Meanwhile, the monster will only do 5 attacks, meaning each character will take 2.5 dmg each on average. So together they can kill 3 monsters, and the 4th monster will be a 50/50 battle. So 4x as strong. And that's not even considering synergies between the characters or anything like that...
So if you're balancing all enemies around a 2 character party, you have to realize that a solo character is going to be 4x weaker than you normally expect. And a solution of "well, just level him up more while he's solo" is not a good solution, because he'll continue to have those high stats when the 2nd character joins, which will just imbalance the game even more.
Personally, I would just give the MC a story-related buff while he's fighting solo. Whether that's some sort of gear that grants him additional stats and breaks later, or a potion that only lasts 1 day, and therefore is gone once the companion joins, or whatever. That way you can keep the enemies at the same stat level while not penalizing the player for the mere fact that the story hasn't granted us another character yet.
Or just cut the solo gameplay entirely. Make it part of the introduction and we just start playing once we have 2 characters.
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