Could one "build" elements? I was wondering this: would it be possible to "construct" elements by arranging their constituent particles in high-energy environments? So apart from just fusion, could you sub-atomically manufacture elements?
 A: The bulk of physics obeys the time reversal symmetry. In QM that means that a process which is allowed in one direction is allowed in the other direction and that the total probability for it is the same in both directions (assuming you can set up the time-reversed final state as an initial state).
So a way to understand the delicacy of trying to assemble a non-trivial nucleus from individual nucleons is to look for the occurrence of non-trivial nuclei (or their excited states) coming apart into individual nucleons.
Alas, as far as I know this simply doesn't happen. 
Which implies that doing it by intent is not merely beyond current technology, but that it is hard to envision what improvements might lead to a way to start thinking about how to finesse it. The time, space and energy scales involved are all extremely demanding.

It may help you to understand that even in light nuclei like carbon the protons have momenta up to the neighborhood of 100 MeV (which is to say they are mildly relativistic), but are confined to a volume a few femtometers in diameter. If you were to shoot a free  proton through that volume with that kind of momentum, it would pass through on a time scale on the order of
$$ t \approx \frac{10^{-14}\ \mathrm{m}}{10^{7}\ \frac{\mathrm{m}}{\mathrm{s}}} = 10^{-21}\ \mathrm{s}.$$
That's a even shorter time scale than the attosecond physics guys use!
