Implementing an analog approximation of an FIR filter given its impulse response
FIR filters typically have a sinc^x type impulse response spectrum or something that looks like it, in some but not all cases. The sinc^x shape is mainly seen when the impulse response h(n), if plotted on cartesian coordinates, look like an even function time shifted where the coefficients are placed symmetrical about the origin. This is a simplistic answer based on a particular type of FIR filter such as a Type I or II. You have not given enough information to give a more specific answer.

So your analog filter would have to look like a sinc^x or some type of comb filter with lobes falling off faster than a typical comb filter. But again this is a simplified answer.

In short it is theoretically impossible to do what you want exactly, or even approximately, but I can't tell you that you cannot somehow come up with a crude approximation, say using delay lines