Homemade GPS Receiver: Cascading LNAs and Band-Pass Filters?
I've connected my RTL-SDR Blog stick to a GPS antenna, and when the LNA bias is on, I see a modest increase in the noise, over the band 1565-1585 MHz. (I used some kind of scanning software, the native bandwidth of the SDR stick is not enough for this experiment.
If you can see the LNA output noise with the SDR, and the antenna in front of the LNA is working, then you have plenty of gain. If the noise floor rise is more than 3 dB, then you are well into diminishing returns.
GPS signals are below the noise for a terrestrial wide beam antenna like the patch, before correlation. (at least, the legacy L1/L2 are). So as long as you are seeing ground noise and amplifier noise, rather than noise generated later in the signal chain, there's no need for more gain.
The digital level you're seeing on the SDR at present doesn't mean anything - it is possible that it's all added within the SDR, burying the external signal well below the internal noise.
Do this simple bias off / bias on test with your SDR first.
If it shows a nice bump in the noise floor, then it's possible that your SDR is letting you down in other ways.