SIDS is very poorly understood, but highest probability seems to be that it’s not germ related but related to breathing (more like complex sleep apnea for infants, where sometimes a baby has a messed up breath response. This tracks with SIDS seeming to have a strong genetic component). For what studies we do have, yes sleeping with the parent seems to have a marginal increase in SIDS, although less of one than things like having a loose blanket in a crib.

Ultimately risk falls off around four months though, so yeah maybe 2.5 months is a bit early to try weird things.