Here are a couple of scope captures showing the inrush current at the primary of
a 500 VA toroidal power transformer. This transformer is in a bench power
supply rated at about 400 VA. The power supply main reservoir caps were
discharged before the captures.

The normal full load operating current is about 4 amps RMS.

In these images the grid voltage is green and the primary current is purple.

Tcur1 shows the current in the primary when the grid voltage is applied at the
peak of the sine wave. There's a small current surge of maybe 10 amps due to the
charging of the caps, but there is no large surge due to saturation of the
transformer.

Tcur2 shows the current in the primary when the grid voltage is applied at the
zero crossing (actually, just slightly before) of the sine wave. You can see the
nearly 180 amp surge which doesn't even begin until 5 mS after the voltage is
first applied. This surge current is so large that it distorts the voltage
applied to the primary by causing a substantial voltage drop in the building
wiring resistance. The DC resistance of the primary in this particular toroidal
transformer is about .5 ohms; that, plus the resistance of the building wiring,
etc., is what limits the current to 180 amps.