Transformer makes an audible noise with SSR but does not make it without SSR
You are using a &quot;random-fire&quot; SSR so it can switch on mid-cycle to allow dimming or power control which you probably don't want.

Figure 1. The upper trace shows the trigger delayed close to the end of the cycle. The resultant effective voltage is low. The lower trace shows the trigger close to the start of the cycle. This will result in close to full voltage. The relationship between phase angle delay and resultant RMS voltage is graphed on the right.
A zero-cross triac, when triggered, will wait for the next zero-cross before turning on and will wait for the current to fall to zero before switching off.

Figure 2. With zero-cross switching the result is that the waveform consists of multiple complete half-cycles.
(Both images are mine and taken from Opto-triacs, solid-state relays (SSR), zero-cross and how they work where you can read a little more on the topic.)
At full power there will be a slight clipping of the start of the sinewave due to the turn-on voltage of the triac. This might be the cause but a more likely and severe one would be your control circuit which you haven't shared with us. If this is weak or arrives late in the mains cycle then it would cause triggering as shown in Figure 1.