What is the activation energy of creating molecular hydrogen from atomic hydrogen?
As porphyrin pointed out, two hydrogen atoms coming together from infinite distance will tend to bond, if the energy of the bond can be dissipated. This is unlike the situation where two magnets click together and stay together (because that interaction hits an absolute minimum, rather than a roller-coaster upswing as in the diagram. Ref 1). Two hydrogen atoms coming together from infinity would be attracted, gain kinetic energy from the potential energy of their separation, come too close, then repel each other - to infinity again. Over and over!

Perhaps instead of thinking of an activation energy, it is more relevant to consider a deactivation energy, which is all the energy that the bond needs to dissipate. You could ask whether it is possible for the two atoms to come together and emit a photon of the exact energy needed to quell the oscillation. Or even a lower energy photon, just to keep the molecule bonded, even if still in a high energy state. Alas! Selection rules seem to prevent this or at least minimize its likelihood, and recombination of hydrogen atoms is reported to occur thru three-body interactions. Ref 2
Can you do this any other way? Perhaps instead of observing them in free space, you could attach both atoms to a metal surface and let them find each other in small steps. Some metals, like zinc, evolve H$_2$ in acidic solution. Very very pure zinc reacts only very slowly with acids. Ref 3 My interpretation of that situation is that when the first evolution of hydrogen occurs, the hydrogen is in atomic form, and is attached (not strongly bonded) to the surface, whether that is actually metallic zinc or a nanothin layer of ZnO, perhaps as a ZnO  -  H moiety. A more stable state would be for two of these loosely attached hydrogen atoms to bind together to form H$_2$, but movement is inhibited (by a high activation energy). In less pure zinc, the presence of cathodic sites (like a little copper) provides a better site for H$_2$ evolution, lowers the activation energy and the process spreads over the rest of the zinc to allow rapid corrosion. Less pure zinc could be coated with a thin film of mercury to provide another surface for hydrogen atoms to be relatively immobilized on, and this also gives a high overpotential (a high activation energy)for hydrogen evolution. Ref 4
Some metals, noble metals which have no oxide layer, like Pt, Au and Pd, enable rapid migration of H$_2$ across their surface (thus not only a low, near zero activation energy, but also connection with a massive metal substrate that can accept some vibrational energy when two hydrogen atoms get together and dance for a while before settling down. They are good surfaces for evolving H$_2$.
A number of organic reactions were done with atomic hydrogen, using high activation energy to prevent  formation of molecular hydrogen; this was classified as due to nascent hydrogen, a term now in disfavor. Ref 5
Ref 1. http://www1.biologie.uni-hamburg.de/b-online/library/newton/Chy251_253/Lectures/LewisStructures/Dihydrogen.html
Ref 2. I. Amdur,  J. Am. Chem. Soc. 1938, 60, 10, 2347–2355
Ref 3. https://en.wikipedia.org/wiki/Zinc
Ref 4. https://en.wikipedia.org/wiki/Overpotential
Ref 5.https://en.wikipedia.org/wiki/Nascent_hydrogen