At what point can Approach mode be engaged in an A320?
The conditions for arming the ILS APPR mode are given in the FCOM:

Arming Conditions
The pilot arms the (ILS) APPR mode (LOC and G/S in blue on the FMA) by pushing the APPR
pushbutton on the FCU, provided that:

An ILS approach is selected,
The aircraft is above 400 feet RA,
The ILS and RA are available,
Go-around or takeoff or final mode is not engaged,
ILS frequency and course are identically set on both receivers.


(Airbus A320 FCOM - Autoflight - Flight Guidance)
These are just the technical limitations for when you can arm the APPR mode, not when you should. The FCTM has some more details on that:

INTERCEPTION OF FINAL APPROACH COURSE
When cleared for the ILS, the APPR pb should be pressed. This arms the approach
mode and LOC and GS are displayed in blue on the FMA. At this stage the second
AP, if available, should be selected.
If the ATC clears for a LOC capture only, the crew will press LOC p/b on the FCU.
If the ATC clears for approach at a significant distance, e.g. 30 nm, the crew should
be aware that the G/S may be perturbed and CAT 1 will be displayed on FMA till a
valid Radio Altimeter signal is received.
[...]
MISCELLANEOUS
The ILS or LS PB is to be checked pressed in the first stage of the approach. The
crew will check that

LOC and GS scales and deviations are displayed on PFD
IDENT is properly displayed on the PFD. If no or wrong ident displayed, the crew
will check the audio ident.


(Airbus A320 FCTM - Normal Operations - ILS Approach)