Mean Wells are notorious for their bad inrush currents. Too bad they don't say for how much the inrush is. Usually 50ms is a conservative duration (since the inrush is exponentially decaying)
You definitely want a T (delayed or slow blow fuse). Pick your favourite brand or standard (like IEC fuses, for example) and look at the I2s curves: you want to survive the surge and the running current (so you need to stay on the left of the curve) but the safety limit (i.e. cable and connector rating) should be on the right of the curve.
As an example, the Littelfuse 213 (IEC delayed) at 3.15A has a thermal limit of about 6A (so in a pitch would be just enough to protect the connector, but no safety margin) and can handle 60A for about 20ms so it's a little too small (you risk thermal fatigue and nuisance tripping). A 5A IEC fuse instead will keep running 10A for hours so it would burn the connector.
There's just no 'standard' fuse fitting the bill, here (also remember that fuses are not precision components, they have tolerances).
In this case you can either a) use a bigger inlet module (rated 10A, for example) or b) use an inrush limiter (these are special NTCs but are somewhat tricky to apply correctly)
In my opinion just use a bigger input module