The CMX-600 was in use by the early 1970's. I think it's the first of what we could reasonably call a computer based video editing system that we would recognize in modern terms.
https://www.youtube.com/watch?v=9bNmsKBqFPQ
https://www.vtoldboys.com/editingmuseum/cmx600.htm
It used a PDP-11 Minicomputer, and 6 hard disks capable of holding a whopping 39 Megabytes each. In order to fit on the disks, the video was recorded in monochrome with low quality. Interestingly, it was stored on hard disks, but the video itself wasn't digital. It was some sort of counterintuitive analogue format stored on disk, where the computer controlled seeking, but the output of the disk was fed directly to analogue video equipment. The minicomputer only had enough memory to operate the control software, but not enough to hold whole frames of the video. A PDP 11/20 maxed out at 64 KB of RAM, but 16 KB was a more typical configuration. Once you had your edits programmed into the system, you used the "edit decision list" file to control VTR's loaded with tapes of the broadcast quality version of the footage and it would automatically assemble the final edit.
So... Does it count? It's fuzzy. It was a non linear computer editing system, where you could seek randomly and playback was all controlled digitally.
But it was also analogue and tape based. The video on the digitally controlled hard disks represented an analogue format, not digitized data. And if you wanted to assemble a full color broadcast quality edit, you did have to go back to tapes. But you could theoretically throw away the tapes and play out the black and white video from the CMX system if you wanted to for some reason, so it's technically not tape-mandatory but that was the only practical professional workflow in 1971.
A descendant of the EDL file format that the CMX system used is still in use today. It's definitely the earliest computer editing system that still has obvious continuity to modern workflows. You could load a 1970's CMX-600 EDL into a modern copy of Davinci Resolve and re-conform it to some digital video files on your hard disk.