Why does hydrogen form on such a long time scale?
Why is the time-scale so long?


The time-scale is so long because the density is not just low, it's virtually nonexistent.

The particle density of any gas can be determined at any temperature and pressure using the ideal gas law ($PV=nRT$). Let's use air as an example. At $\pu{25 o^\circ C}$ ($\pu{298 K}$), and 1 atmosphere, the particle density of air ($n/V$) is:

$$ \frac{n}V =\frac{RT}P $$
$$ \frac{n}V =\frac{(\pu{0.08026 L atm (K mol)^{-1})(\pu{298  K})}}{{\pu{1 atm}}} = \pu{23.9 mol L^-1} $$

Converting to molecules per $\pu{cm^3}$:

$$23.9 \frac{\mathrm{mol}}{\mathrm{L}} \times 6.022\times10^{23}\frac{\text{molecules}}{\text{mol}}\times\frac{1 \text{ L}}{1000 \text{ cm}^3}=1.44\times10^{22}\frac{\text{molecules}}{\text{cm}^3}$$

The density of gasses we are used to dealing with is 18 orders of magnitude higher than the density you quoted. If we have a gas of hydrogen atoms at air density, then the timescale for formation of H2 is:

$$ 10^{15} \frac{\text{years}\times\text{cm}^3}{\text{particles}} \times  \frac{1 \text{ cm}^3}{1.44\times10^{22}\text{ molecules}}=6.94\times 10^{-8}\text{ years} $$

$$6.94\times 10^{-8}\text{ years}= 2.54\times 10^{-5}\text{ days}=6.08\times 10^{-4} \text{ hours}=2.19 \text{ seconds}$$

At "normal" densities, the timescale is much shorter.

The second part of your question deals with the quantum mechanics of the activation barrier to this reaction, which I cannot do justice to at this time.