Is it permissible to make up the pre-prayer voluntary (Sunnah) prayers after the obligatory prayer if they were missed due to establishing the congregational prayer at the beginning of the prayer time, given the availability of other later congregations in the workplace prayer room?

A Muslim should pray with the larger congregation. If the first congregation is the larger one, he should pray with them and then perform the pre-prayer supererogatory (nafila) prayer. If the second or third congregation is the larger one, he should first pray the pre-prayer supererogatory (nafila) prayer and then pray with the larger congregation.