Nonrelativistic spin splitting (NRSS) in collinear antiferromagnets, including altermagnets and compensated ferrimagnets, offers a route to high-frequency spintronics immune to stray fields, but its dynamic control has remained elusive. We demonstrate, using density functional theory (DFT) and nonlinear phononics, that THz laser pulses can achieve ultrafast, reversible control of NRSS on picosecond timescales in antiferromagnets. We derive two mode-selection criteria, accounting for phonon and magnetic wavevector compatibility and inversion parity, to identify which phonon modes can activate NRSS. Our calculations illustrate the creation of NRSS in spin-degenerate NiO and the enhancement of existing splitting in LaFeO₃. While practical implementation depends on excitation conditions, lattice dynamics, and mode coupling, these results establish design principles for identifying materials with stronger and more accessible responses. Limitations imposed by driving fields, phonon damping, and anharmonic detuning motivate further materials screening based on accessible excitation strengths, lattice stability, resonance frequency matching, and favorable anharmonic coupling.