DW will allow you to insert the video by clicking where you want it and choosing Insert > HTML > HTML 5 Video
In this example, start time is 5 secs and end is 20 secs by appending '
#t=5,20' to the video filename.
<source src="yourvideo.mp4#t=5,20" type="video/mp4">
The HTML5 video tag is supported in IE11... even though it's market share is becoming statistically irrelevant. Using a URL parameter is experimental - even for new browsers, so if you really wanted that level of control, a simple script would be the logical answer. But you need to ask yourself a big, fat why? If you want the video to begin at a certain point, you should simply edit the video, or make a copy of it that starts where you want it to. Sounds like you are complicating something that does not need to be complicated.
The HTML5 video tag is supported in IE11
yes, but the parameter isn't
As ALsp says it sounds like your complicating matters unless there is a particular reason why you want to do this? Its a fairly straight forward job to cut a video as required.
Edit the video in Premier or After Effects so it starts at the point of interest.
Upload video to YouTube. Click the Share link, get the embed code and indicate at which point you want the video to start. See screenshot. In this example, the embedded video starts at 1:24 from the beginning.