If we go by USS Defiant, VOY and Prometheus registry numbers (aka, the gaps between them), then the Protostar seems like was actually built and launched by 2380-2381 (9 to 10 years after VOY was lost).
Whether its been already thrown back in time by 2383 (when Prodigy is taking place)... we don't know, but it seems like it very well may have been.
Given its advanced Proto-core/Warp, and the fact Chakotay was seen as captain, its likely he was originally sent to the DQ to either render aid or conduct a training mission with his cadets onboard.
The Protostar then encountered a temporal anomaly shortly after leaving Federation space and ended up over 20 years in the past.