Rust is certainly plenty fast as of today. However, there are areas where C may be able to achieve better performance for various reasons.
we need the fastest language possible
This very much depends on what you’re trying to achieve. If you do a lot of number crunching, I could perhaps interest you in some fortran? It’s not your granddaddy’s language anymore. C and C++ are quite capable all-round languages, which offer enough rope to hang yourself, but are still not without reason the workhorses of the industry. I know a few people from the high-frequency-trading domain that have made good experiences (and fortunes) using Java. Rust is a newcomer language, and while it makes good use of LLVM optimizations, it has some unoptimized places yet (e.g. some regexes may be quite slow).
If I would start a completely new project (and had no company policy mandating java), I would bet on Rust, profile the living hell out of the bottlenecks and if necessary rewrite the hottest loops in C.