Air carrier First Officer reported a low altitude alert from ATC and a unstable approach resulting in a missed approach.

Narrative

I was operating a flight from ZZZ-TUL as the pilot flying (PF). We were set up for the ILS XXL. During our approach ATC descended us down to 2500 ft. We were being vectored for the visual XXL. As we got closer to the final approach course ATC gave us a vector directly to the FAF and cleared us for the visual. Normally I would widen out my base turn to give me at least 1 mile before the FAF to capture localizer and get ready to capture glide slope. I was unable to do this as there was traffic to my right and widening my base turn would put me too close to this traffic. Instead I descended down to FAF altitude of 2400ft and started slowing down to 170 kts or less while configuring to flaps 2. I also went direct to the FAF using LNAV and armed the approach. As we got closer the pilot monitoring (PM) noticed the smart turn using LNAV was not going to be clean for the approach so we decided to activate vectors. Not sure if this unarmed the approach or not based on what led to happen. The PM called out that we were above the glide slope which we are still unsure why as we were prior to the FAF fix and at the glide slope intercept altitude. To compensate for this the PM suggested set a lower altitude 1000 ft. As the PF I interpreted that as 1000ft MSL not remembering the field elevation in TUL is 678 ft. I set 1000 ft and selected Flight level change then went gear down flaps 3 in an effort to catch the glide slope with increased drag. This caused our descent rate to increase by very much at a lower altitude. To fix this I clicked the TCS button to arrest the descent. This was a mistake to do in flight level change as I was hand flying now with auto throttles turned on in a speed by elevator mode. The PM called out the slow speed from the auto throttles being at idle we also got a low altitude alert from ATC and the PM (Captain) decided to take controls and go around. We still don't know why the glide slope never captured as we were at the glide slope intercept altitude.