Is it possible for an observer at Earth's equator to simultaneously observe Polaris and the Southern Cross during an equinox?
The March equinox would be a good time to see both; the September equinox would not. Crux lies roughly between RA 12h to 13h, Dec -55$^\circ$ to -65$^\circ$. For best results, be at latitude 10-15$^\circ$ N so that both Crux and Polaris are well above the horizon, and look between 11:00 and 14:00 local sidereal time so that Crux is near the meridian. That would be around midnight in March-April, late evening in May, wee hours in February, or daytime in July-December.