Air carrier Captain reported receiving a ground proximity warning after feeling rushed to execute a short approach assigned by ATC.

Narrative

Arriving into SDF we had anticipated flying the ILS approach to 17R. When on approach we were given the option of flying either the LOC approach to 17L or the RNAV 17L. I chose the fly the RNAV. The conditions were visual although the visibility was reduced with some lower cloud layers. We had flown on the arrival in and had just been given a heading vector and descent and I had requested the FO to draw a direct to inbound radial line off a fix one from the final approach fix (MORKK). Shortly after the line was drawn another plane was given a vector to a further waypoint on the same approach (RACRR). I instructed the FO to re-enter the approach and draw a line from the further fix just in case they had taken us on a longer downwind. This wound up being a rushed attempt because the Approach Controller gave us an early turn just as the FO was finishing up drawing the inbound course line to the final course with the further fix. We were vectored between MORKK and the final approach fix SLGRR and cleared for the approach at 3000ft. As we were approaching SLGRR I noticed that final approach had not activated and realized that I would need to descend. I pulled open descent and had set 2000 as we were approaching SLGRR about 300 feet high if I recall correctly. I had to re-engage the approach mode as it had kicked off. As we passed the final approach fix the approach nav and final were still armed in blue but were not capturing. We had broken out into visual conditions; however; the airport was still not in sight. As I was asking the FO if he could see the airport; I received a GPWS 'obstacle' at which time I immediately commenced a missed approach. I instructed the FO to request the ILS 17R and we were promptly vectored accordingly and made the approach and landing without further issue. When drawing the inbound direct to radial from a fix it's not ever a bad idea; in my opinion; to select a further point as the course will properly sequence provided the approach mode is activated. Also; even though I had planned on flying the ILS 17R originally; I should have briefed the RNAV 17L in advance as well. The D-ATIS was not specific on the types of approaches being conducted; however; the 17L glide slope inoperative was a NOTAM- in the release. From now on I will not accept an RNAV approach; or any approach for that matter; unless given ample room to conduct without having to rush. It would have been much more prudent on my part to ask for a delay in the short vector to set up accordingly.