@woods30 Honestly, I don't think it really matters as long as your first entry comes in before the last day. This means start as early as you can but not necessarily within the first minute that it is open. Just remember, the longer you wait, the more likely the chance that someone in the contest will nab up your name ideas if you're one of those ones that follows the brief and enters safer names that stray away from the obscure. Obscure names rarely make it around here anyway.
I rarely get a chance to get in on a contest the moment it opens, but given that I am one that hovers mostly with no thank yous -- it doesn't seem that I know any of the best formulas for entries. But I do think you have landed upon a good method here. Waiting just a bit allows you to give the CH time to see the type of entries that they are going to get and this can work for or against you, but this also allows you to see what type of CH the CH is. Are they the ones that are going to downrate everyone unless something jumps out at them, or are they being more fair and really giving things thought? You don't know until they actually start going through the entries. This is still iffy though because CHs don't seem to understand the impacts of their ratings, the need for them to go through them as quickly as they can, and to actually read our comments that we submit with our entries so they understand out thought process. Hopefully the newest implement that @RachelSH has spoken of will help with these issues on giving guidance on how ratings here work and hopefully include these aforementioned points somehow so that the rating process will be more beneficial to everyone.
But, I am rambling and I'm sorry. I think to wait it out a few hours or even a day is good, though. Because it allows you to get an idea on several things and it also gives you time to brainstorm. Just because you wait it out to submit doesn't mean you can't already have been brainstorming ideas out. You're just waiting and observing to see if the direction becomes more detailed, to see how active the CH will be, how fair the CH will be, and also gives the CH time to see that their specified direction and interaction is going to curve the kind of entries they get and then it lets you slip in, hopefully more to your favor than those that submitted 15 within the first 20 minutes and are just bouncing ideas. It may work in your favor, it may not. It depends on how creative you are and how mainstream your ideas are and whether the CH wants creative, mainstream, or not and how they have faired with their first 100 or so submissions they have seen.
Edit to add: I also don't feel very hopeful when I see that there have been 5-10 or more loves and a lot of no thank yous and such and those I may only enter just one or two. So if you feel that way, don't no enter but maybe enter just a couple and see how you fair and then go from there. For me, I also stay away from contests if a certain creative or certain creatives are in the high ranks. Why? Because for me, at that point I already know what I am up against and have observed the styles of those creatives and figure if they are going for those styles that mine is going to possibly be more obscure and less helpful to the CH, so why waste the CHs time. That's just me, though.