Well, "a day" is a human-created term quantifying the duration of a 360° degree rotation of a celestial body around its (roughly geometric) North-South axis. So when was "the first day"? Given that it's a human term conceived here on Earth, I'd say it was probably when Earth itself was formed. As for "when time begun", that's somewhat of a self-contradictory question -- the word "when" in the question denotes a point in time, and thus assumes that time already existed "when time begun".
Time manifests to us as a progression from one event to another event, but at the physics level, time is one of the dimensions of the space-time continuum, and there are multiple parallel time lines and thus also multiple parallel realities -- i.e. multiple space-time continua. The latter however is still contested by most mainstream physicists, as the consensus is that there is only one space-time continuum within this universe, and only one universe. As such, "the moment when time begun" would lie within the Big Bang, which is the accepted mainstream view on Creation, when -- again, according to mainstream science -- the wave function of the ultimate quantum singularity collapsed.
Now, as for why everything played out so that when you're looking at your clock, you see the special "
11:11" time stamp, it gets more convoluted. First of all, there's the fact that the measurement of time in hours, minutes, seconds, et al is a human concept, and that this measurement scale is specific to Earth. Secondly, time -- in the sense of how fast or how slow it elapses between two events witnessed by a single observer -- is subjective
to that observer, and in two very distinct ways:
- It depends on the observer's frame of reference. Velocity and acceleration -- which includes gravity -- both influence the passing of time, and thus time passes slower for someone here on Earth than for someone on board a spaceship out in deep space. Various tests have already been conducted with synchronized atomic clocks -- different altitudes, stationary versus travelling at high speed, et al -- and all show that the phenomenon of time dilation as predicted by Albert Einstein does indeed exist.
- The sensation of how much time has elapsed also depends on neurological and psychological factors. We all know the saying, "Time flies when you're having fun." This, too, makes the progression of time a very subjective manner, and this is especially the case when you're all alone, without anyone else there to bounce your perception of reality off of.
However, the question as to why you saw "
11:11" on your clock doesn't necessarily have anything to do with time. The number "
11:11" has a special significance -- it is a number symbolizing the cosmos, among other things -- and so the question should more appropriately be asked as "Why did I look at the clock when it was showing that particular time?" Well, it could be that your inner self decided to look at the clock at that particular point in your subjective time, or it could be that (something in) Creation -- a "spirit guide", the cosmos itself, you name it -- decided to nudge you into looking at your clock by firing a few neurons in your brain.
Therefore, ultimately, the concept of time is irrelevant in this regard, because the real significance of the event you've just described is that you were somehow meant to notice that number, "
11:11". And
that, is a message that you yourself will have to interpret, because it was quite obviously meant for your eyes.