You can check in at the Fort as early as 605am (trust me it's deserted). I usually pull in about 630am (still deserted).
Honestly 9-10am is the latest I would say it's not busy at check-in. Folks don't have to check out till 11am and the procession of vehicles rolling out on busy days is a steady stream till about 1130am. By 11am I would say the arrival side starts getting active.
We've done Lake Louisa the night before and then headed over to the Fort many times. It's 30 minutes from the LL campsites (which are well back in the State Park) to the Fort check-in. To maximize your chances of getting your site, the Fort rolls over to "the next morning" at 605am as I said. That's why we get there at 630am. The early bird gets the worm.
I'm a "specific site" kinda guy (because I know the loop I like pretty well) so I tend to arrive sooner rather than later.
Bama Ed
PS - in all honesty, when you arrive really early, if you want a specific site or sites, you might end up waiting a couple hours for the chosen one to get vacated, blown, cleaned, and prepped. Miracles do happen the less specific you are. But don't count on getting on the chosen one at 635am.
PPS - "Ed, you say the early bird gets the worm". What do you mean?
I like loop 100. I know all the sites and numbers and whether their inside/outside big or small (although I have a popup so not that it matters). So if 116, 126, or 102 are available at arrival, great I will take any of them. But if they aren't available but the folks on 116 and 102 are leaving the day I arrive, I will wait for one of those if I can. But if Michael arrives before me, checks in and gets (and waits for) 116 then he's got it (even if he has to wait). The Jim arrives before me and gets 102 and is willing to wait for it then he's locked in. Finally when Ed rolls in later that morning all that's left is a site in 200 (no more 100 left). No more sites in 100 at all. So you can't really set a time as to when it's too late or early enough. I just get there as soon as I can and take what is left.
And if you're happy with whatever loop you get, you can probably get to your site sooner. I'm happy for you. It's a tradeoff and if it's not important to you then it's not worth it.