That's weird... apparently there's no English term for this exact phenomenon, but there is one in German: Einschwingvorgang (pronounced eyn-shving-fore-gung). Wikipedia wants to have it translated with transient, but I disagree. A literal translation would be “oscillation start process”, i.e. it describes the start of an oscillation which then just goes on, whereas a transient describes an event that's triggered at a discrete moment in time and also has only influence over a limited amount of time (like a piano note).
[Ok, of course the gong is in fact triggered at a discrete moment and the tone doesn't last forever... but bear with me. In case of the gong, both einschwingung and transient apply!]
“Slow attack” is how synthesizers may simulate einschwingung, but it's not really a good approach. An ADSR attack works by having the oscillator start immediately in full swing, but only gradually turning up its signal (envelope). This does work well to simulate transients, but not einschwingvorgangs, because in these is it the oscillator itself that only develops its vibration over time.
Now, synthesizers also use the envelope technique to simulate decay, which is in physical instruments also a behaviour of the oscillator itself. Why then am I making a fuss about einschwingung being more than just attack?
Einschwingung is physically related to “decay in reverse”, indeed it is often described this way – but IMO that's a bit misleading. Decay is (or at least, can be) a purely linear effect, for example a decaying piano string is for all practical purposes linear. It is the linearity that guarantees the whole process can be simulated by a non-decaying oscillator followed by a time-dependent amplifier/filter, because for linear behaviour putting in a mixture of modes at the start is equivalent to putting in each individual mode and mixing the results★.
But if einschwingung were linear (more precisely, LTI), the volume would either just keep on growing and growing until infinity, or reach a maximum amplitude and decaying back to zero before growing again, repeat... this is clearly not how instruments behave (though the former is a pretty good description of feedback in amplified audio).
Instead, the einschwingung in gongs and also in bowed strings and many others is a fundamentally nonlinear effect. That means, you have energy transfer from some “quiet” mode into a more audible one. On a piano/guitar string this is not possible because it's too linear – it would be the equivalent of playing a 2nd harmonic on a guitar string and it then changing into a 3rd harmonic†. But that is essentially what happens in a gong: the beater initially just perturbs it in a very low-pitched mode that contains a lot of vibrational energy but is almost inaudible, but this energy is then transported into the much louder white-noise-ish modes.
In bowed strings, it is the bow-hair–string contact that behaves nonlinearly. Specifically, increasing the sliding force 2× does not increase the sliding speed 2×. Instead, up to a point the string sticks completely to the rosin and then it's suddenly released. At the very start, the result of this isn't really an oscillation at all but more of a random/chaotic scrape – but then resonance kicks in and creates a phase-locked loop, which is what creates the actual violin tone. But the einschwingvorgang, or the transient that results from it, isn't really a tone at all and therefore can't be convincingly simulated with ADSR envelopes. It can only be simulated with nonlinear elements – the simplest of these are ring modulators and frequency modulation. The best known synth to use this approach is the DX-7.
★One way to see that a gong is non linear is to compare striking it a couple of times gently and each time waiting for the low-pitch mode to decay again, which striking it with the same intensity in quick tremolo. If the gong were linear, then the tremolo would just sound like each of the single strike in succession, but instead it will actually change its character and develop the swoosh that you also get from a harder hit, because the small hits accumulate until enough energy is in the system so it becomes nonlinear and feeds into the high-frequency modes.
†Pianoteq actually has a feature that simulates this kind of behaviour – if you turn it on, your piano will suddenly sound like steel drums!