Ever tore into a DVD burner driver? Trust me, the DC bias comes up sloooowy... It may not be 15 seconds, it may be on the order of milliseconds, but it IS there.
The soft start is built into the current mirror startup circuits in the chip itself.
Transient analysis is a huge part of Electrical Engineering training. It may not be stated on the data sheet, but it is assumed you learned to get control of your circuit's startup state in school.
If not, you'll learn about it quickly in your first design review at your first employer.
I know I was white faced when I watched an audio design engineer start penciling in roll-off caps on one of my first commercial designs where I didn't think I needed them. He said "Well, if you had not already bypassed the power correctly, I would have fired you on the spot". He spent a long, long, time with the calculator penciling them in. From the stares of my new co-workers, I received the message. Later he told me the other reason he continued with my employment was that I at least prototyped unit one, and he had stopped by to listen to it without my noting... I am self taught... I do have a degree, but not in what I do.
I had worked really hard to ensure I had a clean start, but I assumed one input reconstruction filter with roll-off between the audio DAC and the amplifier chain was enough. Zorched in the first thirty seconds in design meeting one...
Some place there is a DOD spec on audio roll off I was not aware of, and this was to be a low cost, mass produced, product for DOD. Needed or not, the spec calls for HF bypass to limit turn-on thump. Not good to tell the other guys with guns, where you are on start-up.
I have a large pile of dead, single mode, red diodes on my desk where what is widely regarded as the best low cost analog driver in the world had a bad batch. Culprit after staring at the board for hours, one slew rate limiting cap, was too small in value.... Second problem, I assumed that because the past ten drivers were good, the next four ordered would be fine. Moral of the story, incoming test is important. Usually I would have tested each driver with a dummy load and a scope, then with the sacrificial bench diode. Instead of taking care, I put a one Ohm resistor on them, set the Imax with full input and a current limited bench supply, and hurriedly hooked them up. Diodes blew before I ever even saw any laser light.
The diodes stay there to remind me, that watching a whole paycheck vaporize is not to be tolerated. All of them have a mirror faucet blown off.
My point is...
You may not see it on the data sheet but it is there by implication.
Listen carefully starting at 4:05.. You need to make sure the control circuitry is stable before applying power to the diode.
Steve