Sonata form. No doubt about it. The fact that it’s a concerto written by Bach points clearly to it, but upon further examination, I found a clear exposition, development, and recapitulation.
The main theme (theme A), of course, is in G major, and moves between tonic and dominant (D major) as expected. There is a theme A’, which is a repeated version of a truncated theme A. These two themes, A and A’, are the most prominent throughout the movement.
At the development, theme B emerges. There are lots of interplay between diminished and major chords, often switch back and forth per measure, all the while keeping the same arpeggiated rhythm. Bach, as the clever composer that he was, sets up for the B theme in the relative minor (E minor) by playing this arpeggiated rhythm in D# diminished, which provides the leading tone for the harmonic E minor.
The development then switches to the A theme in minor, then to the A’ theme in minor. The A theme then returns, except this time it is much sparsely orchestrated. At the same time, Bach expands the melody of theme A, making it longer.
Up next is a thickly orchestrated transition, with high strings playing arpeggiated chord tones while the low strings lead the descending scales to another repetition of the B and the A’ theme in minor.
Everything leads to the recapitulation, as it should, and things are quite straightforward from there: theme A is presented in the tonic key of G major to finish off the movement.
I noticed that the rhythmic figure of a dotted eighth plus a sixteenth, especially when done in tutti, signals a large arrival point for the music. This is characteristic to Baroque music. Also, as is characteristic of Bach, the movement at multiple points repeated the melody in different voices, descending in pitch.