That's one of @Brent trees. Be really careful with it - I have struggled with cork bark pines; they seem much weaker than the standard JBP. Given the depth of the pot, I'm not sure I would move it into a final bonsai pot in one step. I would probably do an initial repot into something too large - checking the root health and minimizing the depth while working on spreading out the roots that are right now going down in that pot. I am curious to hear what others recommend.
That pot would not be my choice for that tree. Very feminine. You are likely going to end up with a very strong masculine tree with a thick gnarly corky trunk, so you want to go hardcore masculine. A heavy deep rectangle (assuming you plan to keep it short). Something like:
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I'll find some photos of a few corkers I've reduced from deeper pots; including a cutting-grown one from Brent. That pot is fine as a step-down pot, and while you're deciding on a front, but probably is not aesthetically the final pot.
In short, you will find the roots run deep and fairly stout, so they'll need to be reduced a little over time. You'll also find his soil will need to be replaced with something that stays drier. He uses bark and pumice, which is ok when you're in the nursery trade, but it does break down into a fine texture that pine roots don't like. Long-term, you will need something that dries faster and offers you more control over watering.
This was a 2-gallon cutting-grown Hachi Gen from Brent. I think I got it in 2008 or 2009, and repotted it in 2011. Here are some shots of that first repot:
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See how the big roots run straight down, under a tangled mess? It's probably all you can hope for when you're dealing with a cutting-grown corkbark black pine, but you need to reduce those big roots a few at a time, and replace the broken down soil directly under the trunk as quickly as you can to prevent rot.
I would wait until next year, because it's growing pretty strongly right now. Another year won't hurt at all.
It should work into a 4" deep pot, but it's really hard to tell looking at the photo, and without a look at the roots.