After testing this your initial code snippet here, the following also starts the video at 10 seconds:
<video preload="metadata" width="320" height="240" controls>
<source src="video.mp4#t=10" type="video/mp4">
</video>
The WEB Core code does the equivalent.
Not sure why the playerNameVideo.CurrentTime := 0 does not execute for you properly, it changes the time correctly in our test case. But by setting the CurrentTime the thumbnail also changes.
I don't think there is a way around this other than somehow obtaining the required image/thumbnail from the video and setting the Poster property to that.