FCTM: 'Autopilot Engagement-One Engine INOP'. "when at a safe height, >400' agl, the autopliot may be engaged
When they write "safe height",they mean MFRH.
You need to keep TOGA thrust (SE TO(except in vnav t/o)or Simple 2 Eng GA) until you have cleared the t/o path obstacles.
If you engage at 400 feet(technically possible but if 400 is below MFRH) you will engage a pitch mode that will aim for your mcp speed rather than the required GA pitch,you need that pitch to satisfy obstacle clearance.
Your thrust,if AT is engaged will go to climb thrust rather than the required t/o thrust until MFRH.
Engaging AP below MFRH is poor practice that is creeping into practice and normally pushed by trainers or airlines who have no trust in their line pilots handling of a basic pitch with FD.
Engaging the AP which opens the mcp window will require also more work from the PM who will have now to select UP speed or required speed,rather than just retracting the flaps step by step.
Engaging as soon as obstacles are cleared,depending on the complexity of the GA maneuver,airspace... could be done,but briefed for obvious reasons.
I prefer to re engage the AT first after flaps are up then and only then re engage the AP.
So im a BBB .....unless situation dictates AP ON for easier position /maneuvring awareness(ie complex EOSID/GA) but never never below MFRH.