You might want to read up on the Friis Noise Equation which is a method of describing the contribution of each stage of a receiver chain to the overall noise figure. The short version is that the first couple of stages in the chain have a much larger impact on the overall noise figure than later ones, so using a good LNA next to the antenna gives the best performance.

If we take a very simplified model, with some arbitrary figures:

Assume we have an antenna feeding a length of coax that has 3db loss and a noise figure of 3dB, feeding a filter with 2.5dB loss (like the FA one, with 2.5dB NF) the receiver which has its own internal amp set to 40.5dB gain and let’s guess a noise figure of 1dB. The overall gain is 35dB with an overall noise factor of 6.5dB.

If we now put an LNA such as the rtl-sdr one in the chain, which has a gain of 26dB and noise figure of ~1dB, before the coax, then reduce the gain on the in built amplifier to 14.5dB so that the overall gain is the same at 35dB. The noise figure has dropped to only 1.03dB.

There is a calculator here which you can put your own figures in to see how they affect things. In reality it’s more complicated since amplifiers and filters are not perfect, receivers usually have a few more stages than just an amplifier, and an amp like the rtl-sdr one has several stages of filtering and amplification. It should serve to illustrate the point though.

There’s also this article which talks about positioning of amplifiers and the effect on performance.