Splicing H264 is difficult to do, due to the nature of long-GOP encoded typically in use. Long GOPs don't cut well.
If you use Premiere, you'll need to first decode the video back out into a lossless or uncompressed stream (using something like
VirtualDub), then import that into Premiere, cut as needed, and re-encode back out using the Adobe Media exporter. While Premiere can, technically, import many formats, the timeline is almost painful to use or navigate on a compressed video stream.
A more ideal scenario may be to splice without re-encode (or single-GOP reencode, with stream copy for the remainder of the stream). Download
VideoReDo, which I believe comes fully functional as a 15-day trial (with registration), and give it a try. It can edit MP4 H.264 streams the same way it does with MPEG-2.
Premiere is an awesome editor, but I think there are better tools for this specific task. Tools with less net quality loss.