In a historical description of the Stern-Gerlach experiment, [Friedrich 2003] says:

Einstein and Paul Ehrenfest, among others, struggled to understand how the atomic magnets could take up definite, preordained orientations in the field. Because the interaction energy of atoms with the field differs with their orientation, it remained a mystery how splitting could occur when atoms entered the field with random orientations and their density in the beam was so low that collisions did not occur to exchange energy.

They give this quote from Einstein (from a March 1922 letter to Born):

The most interesting achievement at this point is the experiment of Stern and Gerlach. The alignment of the atoms without collisions via radiative [exchange] is not comprehensible based on the current [theoretical] methods; it should take more than 100 years for the atoms to align. I have done a little calculation about this with [Paul] Ehrenfest. [Heinrich] Rubens considers the experimental result to be absolutely certain.

Can anyone explain this? Classically, if we send a beam of randomly oriented dipoles through a Stern-Gerlach spectrometer, we expect an ellipsoidal pattern that is not split into well-defined components. According to modern quantum mechanics, we expect what we get in the famous postcard Gerlach sent to Bohr, above.

So apparently Einstein was working in a theoretical universe that was very primitive and contained only a subset of modern quantum mechanics. However, this subset must have contained "space quantization," i.e., the quantization of angular momentum in units of hbar along a particular axis. I guess this is what people refer to as early quantum theory. At the time, electron spin was unknown, and the Stern-Gerlach result was interpreted as a triumphant proof that the orbital angular momentum of the odd electron in the silver atom had the two values $\pm\hbar$. (Zero was forbidden.)

What was the intermediate theory under which the splitting of the beam into two discrete components was interpreted as evidence of quantization, but Einstein's concern about time scales still appeared? What would have been the reasoning that would have led to this concern about time scales?

Friedrich and Herschbach, "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics," Physics Today, December 2003, p. 56

I came across an explanation of this in a paper that Nick R pointed out, Schmidt-Boecking et al., "The Stern-Gerlach Experiment Revisited," https://arxiv.org/pdf/1609.09311.pdf .

Einstein and Ehrenfest apparently reasoned as follows. Before a particular silver atom enters the magnetic field, its magnetic moment $\mu$ is randomly oriented. Once it enters the magnetic field, it has an energy $\mu\cdot B$. Unless there is a mechanism for the transfer of energy in or out of the atom, this energy can't change, and therefore the magnetic moment can only precess about the $B$ vector, but it can't change its orientation with respect to it. One mechanism for energy loss is Larmor radiation, but this is very weak and would take 100 years to have enough of an effect to produce alignment -- many orders of magnitude too long for the times of flight of the atoms in the actual apparatus.

So what was missing conceptually was the idea that a single atom, before entering the field, could be in a superposition of two different states with the magnetic moment oriented parallel to or antiparallel to the field.