If a soldier did not make the EPS list, but has a clear cut path for E4 to E5 (internal), can they still be promoted?

This is exactly what my situation was in 1969/70. I was authorized to wear E-5 stripes and was assigned to a position with the battalion of great responsibility which was an E-5 slot. On paper (201 file) I was still a Spc E-4 and paid accordingly. Admittedly I had a couple disciplinary issues that may have held me back from being official promoted (the battery commander and I did not get along and that is my fault.)

I was active I had something similar happen with my paperwork where the theater admin unit (G1) for 8th Army failed to submit the paperwork to DA. I watched the list and saw I made points and my name didn’t appear. So I brought the issue up and got it resolved thru an exception to policy and was able to still pin on my appropriate date. The pay took a couple weeks to get straight but it was taken care of ( had to wait for the official approval to get returned from DA). It is possible but not easy

If it was the admin clerks mistake then the unit can submit a STAB packet, have them look into that. If the Soldier was not promotable at the time of EPS Packet submission they usually will not do a STAB packet. I am not admin, but during my time as a platoon SGT I had to have the admin clerk in my unit submit STAB packets for errors on their part.