Well I would, taking off the lowest branches certainly, and possibly the next tier, although the picture isn't very clear when it comes to judging which branches are coming from where in the lower parts. That would still leave some halfway down, but as the top is a bit sparse, and it's already July, I'd leave those in place till next year and remove them in late spring, or when the weather has warmed and growth is happening (which might be early spring where you are).

UPDATED ANSWER

Cover those thin roots back up immediately - they should not be exposed like that. I think the point someone else was trying to make was that any mulch laid over the top of the soil should not be in contact with the trunk of the tree, but it's absolutely not a good idea to expose fine, thin roots like the ones in your picture. Don't allow the soil you replace to sit higher against the trunk, that's the only thing to watch for, along with the same rule for any mulch you choose to use.  Much later on, as the tree matures, you may find large roots appearing above ground of their own volition (hopefully not because all the soil's been washed out by torrential rain, I don't mean that) and those roots should not be covered up. This, though, is unlikely to happen for some years.

Otherwise, my advice remains as above, that is, to remove the lowest tier of branches now, leaving any other pruning/shaping for next year.