This is somewhat unusual thing to ask, especially because there is hardly anything regarding the beginnings of xenoarchaeology written in-game. What do you think? When did humans first begin to systematically seek the ancient remnants of the Daam K'Vosh?
Two options, Xenobiology as whole could be considered as starting after humans found alien organism, which was prolly before they found Valhalla. If you mean of some higher developed alien organism then it's of course Valhalla.
PS: Since VH is a first source of knowledge about DV, then right after.
Possibly soon or right after they stumbled on first alien ruins. As for dates, don't know, most dates are obscure in the Freelancer universe.