So, I was recently making a character, and my lore for WH40k is a bit sparse. One thing I was wondering is if there is a minimum age that people can 1) become a psycker and 2)participate in the soul-binding ritual for astropaths occurs.

I wasn't sure if psycker powers generally didn't manifest until puberty or if the soul-binding was restricted to 18 and older only or something like that. For the soul binding in particular, part of me thinks that the Imperium is very traditional and such, and keeping an 18+ restriction might be such a tradition and another part of me thinks that the Imperium basically does whatever it needs to improve itself, and doesn't seem to consider age to be a huge deal (No sparing the children on a condemed world)

The awakening of psychic potential generally happens during puberty although both delayed and juvenile awakenings are far from unheard of. I'll note that such awakenings are almost always involuntary (and the impression I got from your post was that you believed otherwise), with the exception of some rather insane persons' delayed awakenings.

As for the minimum age for a Soulbinding? No such thing. Obviously, a person must be psychically active at the time (for Soulbinding to the Emperor, at least, being bound to a xenos or daemonic entity may well have different requirements, as determined by the GM), and have been so long enough to be identified and collected by the League of Blackships, and at least preliminarily conditioned/trained by the Adeptus Astra Telepathica, but aside from that. the subject could be any age. I believe the youngest even hinted at was a pair of conjoined twins who were soulbound at age 9. The Imperium in general doesn't really believe in age limits in any case (specific planets/cultures within it may do, but plenty don't).
The big limiters on Soulbinding: the Adeptus Astra Telepathica has to believe that the person in question is sufficiently healthy, both physically and mentally, and that they have sufficient psychic strength for it to be worthwhile. They also have to be fairly sure that the subject is without taint. Provided those conditions are met, they will attempt to have them soulbound as quickly as possible.

Also, like a psychic awakening, Soulbinding is generally less than voluntary- the ritual is less something you participate in, and more something that is done to you, and is incredibly traumatic.

As Alasseo says, there is really no standard age.

That said, in the Dark Heresy corebook a Sanctioned Imperial Psyker adds 3d10 years to their age (determined on Table 1-11: Age , with ones Home World playing a part in the determination). The extra time represents their time on the Black Ships in transit to Holy Terra ; their testing and training on Holy Terra ; and then their time transiting to wherever the Scholostica Psykana assigns them. An Astropath could conceivably apply a similar idea to them; though Rogue Trader doesn't seem to care as much about the age of an Explorer as Dark Heresy does about an Acolyte.

-=Brother Praetus=-