The best modern take on this development is that multi-cellulars came about as a conglomeration of co-operative multi-cellulars. And, in fact, "fossils" of this circumstance are abundant in, for example, the similarities between the DNA's of certain still-freedwelling prokariotes and their productive counterparts in multi-cellular creatures, such as our mitocondria and plant cell's chlorophyl.
Amongst the reasons you can't find much mineral imprint fossil evidence before multi-cellulars is that there were no mountains rising above the ocean floor, and hence no significant leaching of calcium into the ocean. No calcium, no bones, Sherlock.
"co-operative single-cellulars", I meant to say. Sorry.