The primacy of the major scale happened many centuries after the diatonic scale came to be predominant in Western music. The primary development that led to major tonality was the acceptance of thirds as stable consonances. As that happened, the Ionian mode (previously little used) began to stand out because it happens to have a tritone (B and F) surrounding its tonic major third (C and E). This is the core feature of the authentic cadence which gives us the tension <-> resolution progression that characterizes tonal music. Tonal music practice and theory develop in all sorts of interesting ways, spilling out from that basis.

The transitional period where this happened is roughly in the 1600s.