Go for the timing chain tensioner first! It shouldn't cost you more than $175 to have it done by an MB qualified mechanic.
It has a spring that applies some tension, but oil pressure also plays a part in bringing the timing chain to the proper tension. So judging by your noise at startup...oil pressure seems to be playing-in as a factor.

If the chain tensioner does not remedy your startup noise, then you probably have a worn or broken guide rail, which would require disassembly and reseal of the timing covers both top and bottom....a much more expensive repair.

Hopefully when the top-end was rebuilt, the tech did a competent inspection of the guide rails, therefore reducing the chances of them being the culprit.

Tensioners are on fast lane for $90+/-...Happy New Year.....and welcome back to CA!