Simply put, life hadn't evolved any 'hard parts' yet. This applies to the Proterozoic all over the world, not just in the part of Gondwana that became India.
'Hard parts' usually means tissue that is already mineralized. For example, (vertebrate) bones or (mollusk or brachiopod) shells are made of calcite or aragonite. This material is durable over geological time, so it has time to be replaced slowly by other minerals. Sponge spicules can be made of silica, and can survive unchanged.
The Cambrian period is the earliest time we find fossils of animals with hard parts anywhere. The mineralized parts vary between different types of organisms, so the best explanation we have right now is that a number of organisms independently developed mineralized parts during the Cambrian.
Fossils of soft tissue can be found, but since soft tissue decomposes rapidly, these fossils are preserved by different processes. Although they can often leave some of their original atoms behind as a layer of carbon, it's often just an impression. Sometimes the presence of a lifeform has to be deduced from a trace fossil such as a worm burrow.
Soft tissue fossils are typically only preserved in very fine-grained sediment such as mudstone. Think about how much better a picturre looks on a high-resolution screen than a lower resolution one.
As Wikipedia says:
These formations may have resulted from carcass burial in an anoxic environment with minimal bacteria, thus delaying the decomposition of both gross and fine biological features until long after a durable impression was created in the surrounding matrix.
For most of the Proterozoic, all we find are stromatolites caused by bacterial mats capturing particles of sediment. There are hints of multicellular life from the mid-Proterozoic usually interpreted as impressions of algae. But the most unambiguous fossils of multicellular life appear in a period at the end of the Proterozoic called the Ediacaran (or sometimes Vendian) starting 650 million or so years ago. These include the famous Ediacaran biota from Australia, which give the period its name. But trace fossils and what appear to be early bilaterians appear as well.
Anyway, none of them contain hard parts. This paper hints that the evolution of hard parts similar to sponge spicules may have been starting in the Ediacaran biota, but it's unclear if any of those organisms are the ancestors of anything that came later.