A single-VANOS E36 (the M50TU and the M52, so your 328i) that clatters on a cold start, a marbles-in-a-can or light-diesel rattle that is loudest around 1,000 to 3,000 rpm and fades as it warms, has a worn VANOS, and it is not the emergency the noise suggests. I reassure a lot of people about this one.
Single VANOS is a simple unit. The rattle comes from the anti-rattle spring and tired seals, the seal kit is cheap, and cars run for years like this. Alongside the noise you will usually notice a slightly rough cold idle and a softer mid-range.
I fix it when convenient rather than treating it as urgent, but I do not ignore a rattle that is clearly getting worse.
One thing not to be scared by: this is a different and far milder thing than the E46 M3's dual-VANOS trouble. S54 horror stories do not apply to an otherwise healthy M52.
What you want for the fix is a VANOS seal and rebuild kit.