B787 Captain reported avionics malfunction during approach to land.

Narrative

On final approach to the ILS Runway XXR; we were given direct to ZZZZZ (Outer Marker) at 1800 ft. and were told that we were cleared for the ILS Runway XXR approach. The ILS had been earlier identified as valid (IZZZ). At that point we were approximately 7 miles from ZZZZZ; and the PF (Pilot Flying) armed the Approach (APP button). The autopilot was engaged. At this point the LOC immediately captured the LOC. I was the PM (Pilot Monitoring) and felt at this point that the LOC captured very early given our 45 degree intercept to the LOC and still had another 7 miles to go before the LOC should have been captured. We had set 1800 ft. (Outer Marker altitude) in the MCP. Somewhere along the way; the Glide Slope captured and also commanded the airplane to descend below the 3 degree glide path. As we got lower to approximately 1350 ft. and still not as yet at ZZZZZ; I mentioned to the PF that I felt that we were low. At this point; the PF disconnected the A/P and began a gentle ascent back to the Outer Marker altitude of 1800 ft. ATC subsequently advised us of a 'Low Altitude Alert'. Once we reached ZZZZZ; the PF joined a normal and stable descent to an uneventful landing.After engine shutdown at ZZZ at the gate; I discussed this event at length with the PM. Neither he nor I understood why the automation led us astray in this manner. I was told that we had done everything correctly.....A/P; A/T's were on; APP was engaged; ILS identified correctly. The team is also at a loss for how this event occurred given the data that they received from our aircraft onboard avionics readouts. Both the PF and I are relatively new on the B787; so we are unaware if other B787 pilots have experienced this type of occurrence. I hope to ask around the B787 training team and associated check airman for more possible information of similar events happening to other B787 pilots.Further look into B787 avionic ILS malfunctions related to capturing the LOC/G/S and that relationship to the altitude set in the MCP (Mode Control Panel).