Aim is to avoid the very short overcurrent of the tube filaments. The flash like glow up is not good for the tubes.

(Because somebody in a Forum said: This glow up has been planned in by the clever Philips engineers. SURE they have! But they never planned with tubes which lasts forever. Just think about why tube tester tests first for shorts at the filament…)

The circuit is an easy turn on delay, where an 330Ohm 8W (self-extinguishing) resistor is blocking overcurrent for 3secunds till the 6.3V AC filament power supply (actually is -4V with the 330Ohm resistor ) is loading the 47uF capacitor via the 120Ohm to turn the solid state relay on, to power up fully the amp.

The SSR I used (RP1A23D5):

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Note: On the pics I connected the cable after the fuse. This is incorrect! Bears the risk that if the filament blows the fuse, the resistor gets too hot. So as wrote above connect directly on the transformer, maybe use an small fuse(less than 100 mA) to be really safe.

And finally the glow up of Miniwatt tubes to develop some fear on tubes whihc do cost 100EUR/pcs (Miniwatt glow up is much bigger then with newer tubes… ):

Video