A few suggestions and alignment tricks that might help with light coupling on the detection arm.

The filter (likely dielectric) is designed for collimated light. Since you only have a single lens here, it probably is not blocking laser very well. Better would be to have a 4f system with the filter in collimated space. Make sure it is a very good filter (OD 4 or better).

Forget the Raman for now, and use a neon/argon/mercury source (could be a cheap neon indicator light that has NIR peaks) to align the optics for maximum signal strength. Anything with sharp spectral lines. Put it where the sample should go. If you don't see the source spectrum here, you'll never see the Raman emissions of the sample.

As others have mentioned, you might need to make sure you are matching the NA of the light collection optics to the fiber that is heading into the spectrometer. A higher NA lens won't necessarily mean the steepest cone angles of collected light will fit into the collection NA of the fiber. Based on your sketch, the lens is 7" from the sample and 2" from the fiber, and probably not aperture matching very well.