Is this as in the Character Creation Screen?
If so, maybe you could get the Player's name, and wait until it's changed from "Prisoner" to something else?
Maybe use the OnGetUp event on the chopping block? It's a bit later, but probably early enough, as the player controls haven't been released yet.
Or maybe even a trigger around the chopping-block: parent it to something which gets disabled at the end of Helgen, and just check the one activating it is the Player.
Ah, so it does. I thought GetDisplayName() was vanilla...
Hmm, could you check for Helgen being 'cleared'? I'd assume LAL modifies Helgen to the Post-CharGen State; I know that's what I did in my Alternate Start you could check if something is enabled (like the ruined Inn), or if a suitable Quest Stage is set?
One last, inelegant solution: "Start Necklace" : an amulet the Player can Equip once they have their Inventory. You'd have the issue of people not equipping it and complaining, but it'd work with anything. I think you get Inventory Access as soon as Hadvar cuts your ropes, right, just after entering the Keep?