As to a solid state amp if you have measurable or auditory changes in the performance of the amp after it has been on for 2 seconds, then you paid too much for it, whatever you paid.All components on a circuit board are rated. Those ratings are established once they have warmed up and stabilized from a cold turn on. Once they reach that optimum operating temperature range, then it works as intended, and that takes a lot more than 2 seconds.
Same for tubes.
All the best,
Nonoise