Is there a way to construct FIR analog low-pass filter? (By this, I believe I am asking for no-pole analog low-pass filter, in terms of Laplace transform.)
You have to clearly define what you mean by an "analog FIR filter". "No poles" is not correct because (discrete-time) FIR filters do have poles; they are just all at the origin of the $z$-plane (for causal FIR filters). Note that filters without poles do not exist. Take as an example the discrete-time transfer function
with a zero at $z=a$. Obviously, $H(z)$ has a pole at $z=0$. Similarly for
which also has a zero at $z=a$, but a pole at $z=\infty$.
If you mean transversal filters implemented as a tapped delay line, then you can find analog versions of it, see e.g. this paper.
If you literally mean a filter with a finite impulse response (FIR) then, technically speaking, such a thing does not exist in the continuous-time world. But of course, any stable system has an impulse response that decays sufficiently fast such that for practical purposes it may be considered as zero (or unmeasurable) after a certain time. The discussion if such a system should be considered as FIR or not is moot.
You can build the analog system
which has a finite impulse response, no poles, and an infinite number of zeros. (The pole at the origin cancels.) The time delay can be implemented using an analog transmission line, and the integrals and subtract using an op-amp. FIR analog systems always seem to have an infinite number of zeros.