Double check to make sure that you installed the disconnector spring, with it large coil side down into the trigger slot.
If the disco spring is installed correctly, then it could be that you have burs, which is not allowing the disco to release the hammer on trigger release instead.
To confirm this, after you fire the first shot and the trigger will not release the hammer, flick the selector from fire to safe, then back to fire. If this resets the hammer so the trigger will release it on the trigger pull, then removing burs show below will solve the problem. Also, when you install the FCG parts, make sure to CLP all the parts, including the pins and pin channels before you re-install the parts.
Now if we are still no-go on the second round allowing the trigger pull to release the hammer, you need to take a look through the ejection port window, and make sure that the front face of carrier, is tight against the face of the barrel extension. If they are not tight together, then the trouble shoot as followers.
When the first round was fired, did the spent case eject 10' to 15' out of the ejection port? If it did not, did you remove to use a chamber brush with CLP to clean the chamber before the rifle was every fired? After you cleaned the rifle correctly (read the dam manual on how to clean the rig), did you remember lube the upper receiver bearing areas with CLP. If you are shooting reloads, did you sample check the rounds through a chamber gauge to make sure that the case have been fully sized to begin with, and that when the bullet was crimped, it was not over crimped to bulge the shoulder of the case, with the case not longer fully resized.
Next, pull all the way back on the charging handle and confirm that the face of the bolt stops 1/8" to 1/4" in front of the back of ejection port edge. Also, is the last inch of the charging handle pull the same tension as about the middle of the pull, or is the last inch a lot harder in tension instead.
If the bolt stops way before this, or way after the edge instead, you have a problem with wrong parts used in the receiver extension (buffer tube). If a fixed rifle stock, could be that you have an A-1 butt stock in play, and are using the longer A-2 butt stock bolt that is limiting the buffer from coming all the way back to touch the back inside of the tube.
If a carbine telescoping stock, then could the wrong buffer, the wrong recoil spring, or just a receiver extension that was not milled deep enough (read airsoft).
With the rifle unloaded, shotgun the upper open, put your finger in the back of the carrier, and ride the carrier back and forth in the receiver to check for any binding.
Next, pull the charging handle and B/C out of the upper, remove the bolt from the carrier, and with just the carrier with key, reinstall it in the upper and ride it back and forth again. Hence what you are checking for is to make sure that the key is not too wide for the upper slot and binding, and that when the gas tube enters the key about a inch back from the face of the carrier against the face of the barrel extension, did this happen cleanly, or is the end of the gas tube not indexed correctly for the carrier key, and the gas tube needs to indexed correctly instead.
Note, if you need to tweak the gas tube to get it to align with the carrier key, the gas tube should be tweaked over the middle of the barrel, and not back inside the upper receiver at it end isntead.