I plugged this into DeepThink and his timeline is the following:

Total Timeline for Proxima Centauri Mission

Acceleration + Travel: ~21–30 years.

Deceleration: ~30–50 years.

Self-Replication: ~50–100 years.

Infrastructure Build: ~100–200 years.

Next-Wave Launch: ~0 years (after Step 4).

Total (Earth to Next-Wave Probes): ~200–400 years (optimistically).