Why do LPMs peek at around 30s?

I have seen a number of 445nm LPM test graphs on here and noticed the peek power output is reached after about 30 seconds. For the first five seconds it does not appear the laser even reaches 50% power. I am wondering why. Does the laser actually get brighter as its been powered on for a bit of time, or is it just an abnormality with the LPM?

It's because the LPMs used here are thermal-based. This means that you need to give the LPM time to heat up to equilibrium, meaning that power in equals power out, giving you a constant energy amount stored in the thermopile. When the LPM is at equilibrium, that's when you have a true reading of the laser's output power. Until then, the LPM is capable of radiating out more energy than it has stored, so its not giving the full output power as a reading.

Yes. Wolfman is totally correct. It is the thermopile sensor that reaches "stability" and reflects a "stable" laser reading.
In reality, most DIY lasers hit peak power within a second of turning on (depending on driver/source, etc.)
Video of Ophir head LPM:

You can see (poorly) that the display get's up to 1.2W in less than 3 seconds 1:08.

And here; Regalis shows us the response time of the Ophir head by blocking and unblocking the sensor ~1:00.