Raise SNR of pulse signal by passive LC filter
There are a lot of false assumptions in your question, which I won't get into right now, but it depends on what your end-game is.  50% pulse width detection with low jitter or max SNR with area under the pulse or maybe peak timing detection for Doppler tracking with multiple antenna.?&quot;

Like..  Op Amps have a 0 Ohm output impedance due to Zout=Zol/Aol= 300R/1e6 for unity gain. But for a BJT type with 300 ohm effect ive ESR from current limiting, the slew rate is limited to signal amplitude by current limit on capacitance loading and not Zout or the higher GBW.

@analogsystemsrf has the right idea with a &quot;matched filter&quot;  but again it depends on above.
But I have a slightly different approach looking at the pulse width at 50% peak V or PW50 as we call it, the noise resolution and the group delay.
If pulse delay is bad then a high order filter is bad as group delay increases with order of magnitude.
So I decided to use Falstad since it had built in filters for 10th order Elliptical and Butterworth LPF at 1kHz which may be scaled to 1MHz for the scope traces converting ms to us.
The scope traces ought to speak volumes if you understand the above concepts.

Falstad.com simulator also has a PSRG noise generator called &quot;Antenna&quot; which I scaled the gain to get the rough description of your SNR. It may be a little worse than your signal shown below as Signal plus Noise. which feeds 3 filters for comparison from an Op Amp 0 Ohm source impedance.
If you give specs for PW50, SNR, Noise Spectrum, group delay,  delay distortion and PW50,  then I can tell you which approach is best.

Until then which one do you like best?