Headcanons welcome

So, I'm working on a Thor fic, and it suddenly occurred to me: how the hell did Odin and Frigga pass off Loki as their son? I mean, clearly Frigga wasn't pregnant, so it must have been a bit dodgey when they just announced 'oh look, we had another baby'. Especially since the view we have of baby!Loki is not of a newborn, so not only did a baby appear, but one at least a few months old. So, did Frigga go-off planet for a while and come back with Loki claiming she gave birth to him while she was away? Because if they presented him as an adopted baby, I really don't think Loki could have lived that many hundreds of years without someone letting it slip, even if the whole of the Nine Realms were asked never to tell him.

Am I thinking too much about this?