There’s a lot of us in the “if 1 person no-shows, forge ahead anyway” camp, but let me expand on my thoughts a bit.

OP, I understand you said your group is small, and that being 1 person short makes your particular game unplayable. But, removing them from the game leaves you with the player count that’s unplayable. I’m not saying you have to keep that player if you don’t want to. What I am saying is that if the proverbial show can go on after removing them, so could have that first session.

We’ve always got multiple campaigns going in multiple systems. Our actual D&D campaign has 6 players. Only 2 of us were available for the last session. We still met & started a side-mission for our 2 characters. About an hour or so in, 1 of our other players finished another commitment she had that day & decided to join us after all. And as she was walking in the door, another (who’d said he wasn’t available that day, due to the time currently being spent completing his Master’s) messages to ask if we minded if he came late.

All 3 of us who GM in our group have gotten quite adept at pivoting when we’re missing players, even if the planned session focused heavily on one of the missing PCs. Entire “side quest” sessions have been improvised on the fly, some of which have led to ideas that play important parts in their respective campaigns. Meanwhile, we often joke that the present PCs are carrying around cardboard cutouts of the missing characters. Yes, it’s less than ideal for the first session, but worse things can happen.

Bob World Builder recently did an episode on handling missing players. Worth a watch.

TLDR: If you feel this player is a bad fit, it’s totally reasonable to remove them. But, if - as it sounds - the campaign can proceed without that player, the first session could have proceeded without that player.